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Topic: Least common multiple

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Lowest common multiple

Greatest common divisor

Fundamental theorem of arithmetic

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	Least common multiple - Wikipedia, the free encyclopedia
		In arithmetic and number theory the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both a and b.
		The least common multiple is useful when adding or subtracting vulgar fractions, because it yields the lowest common denominator.
		The lcm is the number which has the greatest multiple of each different type of atom.
	en.wikipedia.org /wiki/Least_common_multiple (467 words)

	Lowest common denominator - Wikipedia, the free encyclopedia
		In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the least common multiple of the denominators of a set of vulgar fractions.
		For instance, the LCD of {1/2, 1/4} is 4 because the least common multiple of 2 and 4 is 4.
		The term is used figuratively to refer to the "lowest"—least useful, least advanced, or similar—member of a class or set which is common to things that relate to members of that class.
	en.wikipedia.org /wiki/Lowest_common_denominator (308 words)

	Math Multiples and Least Common Multiples
		The multiples of a whole number are found by taking the product of any counting number and that whole number.
		The Least Common Multiple (LCM) is the smallest of these common multiples.
		The Least Common Multiple (LCM) of a set of whole numbers is the smallest multiple common to all whole numbers in the set.
	www.mathgoodies.com /lessons/vol3/lcm.html (620 words)

	Definition of Multiple from dictionary.net
		Multiple conjugation (Biol.), a coalescence of many cells (as where an indefinite number of am[oe]boid cells flow together into a single mass) from which conjugation proper and even fertilization may have been evolved.
		A common multiple of two or more numbers contains each of them a number of times exactly; thus, 24 is a common multiple of 3 and 4.
		least common multiple is the least number that will do this; thus, 12 is the least common multiple of 3 and 4.
	www.dictionary.net /multiple (226 words)

	Least common multiple: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-07)
		Arithmetic or arithmetics (from the greek word = number) in common usage is a branch of (or the forerunner of)...
		In mathematics, the lowest common denominator or least common denominator (abbreviated lcd) is the least common multiple of the denominators...
		In mathematics, the greatest common divisor, sometimes known as the greatest common factor (gcf) or highest common factor (hcf) of two integers...
	www.absoluteastronomy.com /encyclopedia/l/le/least_common_multiple.htm (1034 words)

	Least Common Multiple/Length (Site not responding. Last check: 2007-11-07)
		LEAST COMMON MULTIPLEThe least common multiple of two or more counting numbers is the smallest counting numbers which is a multiple of each of the counting numbers.Example: What are some multiples of both 4 and 6? Set of multiples of 4 = {4, 8, 12, 16, 20, 24, 28, 32,.
		Another multiple of both 4 and 6 is 24.
		Therefore, 12 and 24 are called common multiples of 4 and 6.
	www.cmsdnet.net /parents/Math/sld041.htm (113 words)

	Math Forum - Ask Dr. Math Archives: LCM, GCF
		A common multiple is a number that is a multiple of two or more numbers.
		The least common multiple (LCM) of two numbers is the smallest number (excluding zero) that is a multiple of both of the numbers.
		The least common multiple of two numbers can be found by multiplying one of the numbers by the prime factors of the other number that the two numbers don't have in common.
	www.mathforum.org /library/drmath/sets/select/dm_lcm_gcf.html (367 words)

	Least Common Multiple
		The least common multiple (LCM) of two integers is the smallest positive integer that is divisible by both integers.
		Since the smallest positive multiple that 3 and 4 have in common is 12, the LCM of 3 and 4 is 12.
		Therefore, the LCM of 20 and 25 is 500 ÷ 5 = 100.
	cse.unl.edu /~jgerar/tutorial/page2b.html (230 words)

	Information on least common multiple
		[1913 Webster] Note: A common multiple of two or more numbers contains each of them a number of times exactly; thus, 24 is a common multiple of 3 and 4.
		The least common multiple is the smallest number that will do this; thus, 12 is the least common multiple of 3 and 4 (abbreviated LCM).
		least common multiple n : the smallest multiple that is exactly divisible by every member of a set of numbers; "the least common multiple of 12 and 18 is 36" [syn: lowest common multiple, lcm]
	www.wkonline.com /d/least_common_multiple.html (137 words)

	Fractions
		The common factors are: 1, 2, 3, 6, 9, and 18.
		The common prime factors are 2, 3, and 3.
		The least common multiple of two or more nonzero whole numbers is the smallest whole number that is divisible by each of the numbers.
	www.mathleague.com /help/fractions/fractions.htm (2719 words)

	Two, Four, Six, Eight - What is the Least Common Multiple
		Define least common multiple, but before doing so remind the students that they already know what the word least means.
		When we put these all together we have "least common multiple." The least common multiple is the least (or smallest) multiple shared by two or more numbers.
		Have the students find the least common multiple of the sets of numbers on the attached worksheet "What is the Least Common Multiple." As the students complete the worksheet, walk around the classroom and look for correct answers.
	www.glc.k12.ga.us /BuilderV03/LPTools/LPShared/lpdisplay.asp?LPID=13565 (625 words)

	BMCC Math Tutorials -- Numbers -- Least Common Multiple (Site not responding. Last check: 2007-11-07)
		You can determine the least common multiple for any two or more numbers by making a list of multiples for each, and seeing what the smallest number is that shows up on all of the lists-- that number will be the least common multiple.
		Making lists of multiples and doing a visual inspection is a handy way to determine the least common multiple for two numbers, but it starts to get cumbersome if you are trying to determine the least common multiple for three or more numbers.
		Therefore the least common multiple for the numbers 6 and 20 is 60.
	www.bmcc.org /nish/MathTutorials/Numbers/n-lcm.htm (1288 words)

	Mighty Multiples--Mathematics: Grades 5-8 (Site not responding. Last check: 2007-11-07)
		The number 8 is a common multiple of both 2 and 4.
		The number 12 is a common multiple of 2, 3, 4, and 6.
		The least common multiple is used to determine the appropriate denominator for adding unlike fractions.
	www.teachercreated.com /lessons/011102cm.shtml (361 words)

	Factoring - Least Common Multiple (LCM) - In Depth (Site not responding. Last check: 2007-11-07)
		The least common multiple, or LCM, is another number that's useful in solving many math problems.
		One way to find the least common multiple of two numbers is to first list the prime factors of each number.
		After you've calculated a least common multiple, always check to be sure your answer can be divided evenly by both numbers.
	www.math.com /school/subject1/lessons/S1U3L3DP.html (313 words)

	Amby's Math Resources - Least Common Multiple
		The Least Common Multiple (L.C.M.) of two numbers is the lowest number that can be divided both.
		Don't let the "least" in the name fool you - the LCM is no smaller than the largest of the numbers.
		The lowest common multiple is 12, therefore it is the Least Common Multiple (L.C.M.) of 4 and 6.
	amby.com /educate/math/2-1_LCM.html (377 words)

	least common multiple Search-e.com \| leastcommonmultiple
		The least common denominator is the least common multiple of the original...
		LEAST COMMON MULTIPLE The least common multiple of two or more counting numbers is the smallest counting numbers which is a multiple of each of the counting numbers.
		Least Common Multiple (LCM) : The LCM of two numbers is the smallest number that is evenly divisible by both numbers (i.e.
	www.search-e.com /find/least+common+multiple.shtml (1498 words)

	Multiple Riddles (Site not responding. Last check: 2007-11-07)
		A multiple of a number is the product of that whole number and another whole number.
		For example, 16 is a multiple of 2 because 2 times another whole number (8) equals 16.
		I am the smallest common multiple of 3 and 4, not counting zero.
	www.rhlschool.com /math5n15.htm (146 words)

	Fractions -- Least Common Denominator - Math
		Remember, the common denominator is the same as a common multiple.
		The least common multiple is the multiple that has the least value.
		For the fractions 2/8 and 1/6, you could use 8 x 6, or 48 as the common denominator, even though the least common denominator is 24.
	www.bellaonline.com /articles/art30204.asp (301 words)

	How To Find The Least Common Multiple (LCM)
		The least common multiple of two or more non-zero whole numbers is actually the smallest whole number that is divisible by each of the numbers.
		Simply list the multiples of each number (multiply by 2, 3, 4, etc.) then look for the smallest number that appears in each list.
		Therefore, the least common multiple of 5, 6 and 15 is 30.
	www.helpwithfractions.com /least-common-multiple.html (328 words)

	Least common multiple: Encyclopedia topic (Site not responding. Last check: 2007-11-07)
		[follow hyperlink for more...]) the least common multiple or lowest common multiple (lcm) or smallest common multiple of two integer (integer: Any of the natural numbers (positive or negative) or zero) s a and b is the smallest positive integer that is a multiple of both a and b.
		The least common multiple is useful when adding or subtracting fraction (fraction: The quotient of two rational numbers) s, because it yields the lowest common denominator (lowest common denominator: in mathematics, the lowest common denominator or least common denominator (abbreviated...
		If a and b are not both zero, the least common multiple can be computed by using the greatest common divisor (greatest common divisor: The largest integer that divides without remainder into a set of integers) (gcd) of a and b:
	www.absoluteastronomy.com /reference/least_common_multiple (560 words)

	Least common multiple (Site not responding. Last check: 2007-11-07)
		The least common multiple is useful when or subtracting fractions because it yields the lowest common denominator.
		If a and b are not both zero the least multiple can be computed by using the greatest common divisor (gcd) of a and b :
		is adequate to calculate the lcm for numbers using the formula as written.
	www.freeglossary.com /Least_common_multiple (562 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The purpose of this paper is to present a proof for the connection between least common multiple and greatest common divisor.
		On the other hand, since the only positive multiple of 6 less than 12 is 6 itself, and since 4 is not a divisor of 6, we see that no other common multiple can be less than 12.
		Because c is a common multiple of a and b, we know both a and b are divisors of c.
	www.american.edu /academic.depts/cas/mathstat/People/kalman/pdffiles/assessment/sample.doc (701 words)

	factoring least common denominator (Site not responding. Last check: 2007-11-07)
		numerator and denominator by the least common denominator of all denominators in...
		The LCD ("least common denominator": "d" in the paragraph above), is the smallest number which is...
		the equation by the least common denominator of all denominators in the...
	www.moreloanshere.com /articles/79/factoring-least-common-denominator.html (526 words)

	Answers to worksheet chapter 4 section 2 (Site not responding. Last check: 2007-11-07)
		The LCM of two natural numbers is the smallest number that is a multiple of both numbers.
		The Least Common Denominator of two or more fractions is the smallest number that can be divided evenly by each of the fractions' denominators.
		The relationship is that the least common denominator is the least common multiple of the two denominators involved.
	www.rose.edu /faculty/gjackson/preal/aws-4.2.htm (748 words)

	Least Common Multiple
		The learners are already familiar with the multiplication facts 1-10 and have already learned to add and subtract fractions with the same denominator.
		Each player tries to be the first to state the least common multiple of the two cards on the table.
		I had considered giving each player a copy of the multiplication table for the numbers two through fifteen but I felt that it would be very difficult for the player to quickly isolate two particular columns (or rows) to find the LCM and would thus interfere with the the reinforcement of the skill objective.
	edweb.sdsu.edu /courses/edtec670/Cardboard/Card/L/LCM/lcm.html (784 words)

	Least Common Multiples (Site not responding. Last check: 2007-11-07)
		The least common multiple of two integers is the smallest integer that is a multiple of both numbers.
		The lcm is the product of all primes that are common to one or the other (or both) of the numbers.
		Then write down multiples of the second until they are larger than the largest multiple of the first.
	www.math.nmsu.edu /~pmorandi/CourseMaterials/LCM.html (439 words)

	Question Corner -- How To Find The Least Common Multiple
		The LCM is the product of all of these primes, each one repeated the number of times it occurs in the factorization where it appears most frequently.
		Therefore, the LCM of the numbers from 1 through 10 will be the product of the number 2 (occurring three times), the number 3 (occurring twice), and the numbers 5 and 7 (occuring once).
		The reason that this is the smallest multiple of every number between 1 and 10 is that, in order for one number to divide a second, every prime factor of the first number must divide the second number at least as many times as it divides the first.
	www.math.toronto.edu /mathnet/questionCorner/lcm.html (518 words)

	Math Forum - Ask Dr. Math
		The question I have is about how to find the least common multiples from a set of numbers.
		Date: 3/30/96 at 16:57:26 From: Doctor Sebastien Subject: Re: least common multiples Hi, The least common multiple (L.C.M.) of a set of numbers is the smallest number that is a multiple of all numbers in the set.
		Here's another way to think about doing Least Common Multiples: Since the least common multiple of two numbers is the smallest number that is a multiple of both the other numbers, you could also think of that as being the smallest number that contains all the _factors_ of the first two numbers.
	mathforum.org /library/drmath/view/58076.html (394 words)

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