Unit: Pre-Algebra Review
Module: Factors and Fractions
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Greatest Common Factor and Least Common Multiples
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The greatest common factor is the largest factor two numbers have in common.
The least common multiple is the smallest number two numbers divide into.
To find the greatest common factor of two
numbers, first find the prime factors of both
numbers. Compare the two prime factorizations
and select factors they have in common. Multiply
these two factors together to obtain the greatest
common factor.
In this case, 6 is the largest number that will divide
evenly into both 12 and 162.
The greatest common factor is also known as the
greatest common divisor.
To find the least common multiple of two
numbers, first find the prime factors of both
numbers. Compare the two prime factorizations
and select each prime factor the maximum number
of times it appears in any of the factorizations. In
this case 2 appears a maximum of two times, while
3 appears a maximum of four times. Find the
product of these factors.
In this case 324 is the smallest number that 12 and
162 will divide into.
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