New York City SHSAT 2017

(Marvins-Underground-K-12) #1

If you need to find a common multiple of two integers, you can always multiply them. However, you can use prime factors to find
the least common multiple (LCM). To do this, multiply all of the prime factors of each integer as many times as they appear. This
may sound confusing, but is pretty clear once it’s demonstrated. Take a look at the example to see how it works.


Common multiple of 20 and 16:


So 320 is a common multiple of 20 and 16, but it is not the least common multiple.


The prime factorizations of 20 and 16 are as follows:


Therefore, the prime factors of both of these numbers are 2 and 5, and the greatest power of each of these numbers is 4 and 1
respectively, so the least common multiple is


20 × 16 = 320


24 × 5 = 16 × 5 = 80

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