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What Is The Difference Between The Greatest Common Factor And Least Common Multiple Of A Pair Of Numbers?

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Suppose you have two numbers, 12 and 18. 12 = 2*2*3 18 = 2*3*3 The Greatest Common Factor (GCF) of these numbers is the largest number that will divide both of them evenly. 12/6 = 2; 18/6 = 3  The GCF of 12 and 18 is 6 = 2*3 The GCF is no larger than the smallest of the numbers.  The Least Common Multiple (LCM) of these numbers is the smallest number that both of them will divide evenly.  36/12 = 3; 36/18 = 2  The LCM of 12 and 18 is 36 = 2*2*3*3 The LCM is no smaller than the largest of the numbers.
For two numbers, GCF*LCM = (product of the two numbers)   6*36 = 216 = 12*18  The Greatest Common Factor (GCF) is sometimes called the Greatest Common Divisor (GCD).

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