Common Multiple

Mom TRYING to check daughter's Pretest (didn't realize I had forgotten so much!) What is the easiest way to find the least common multiple of two numbers? This problem is: What is the least common multiple of 36 and 42...it is a multiple choice question, but I'd like to try to figure it out myself (just in case I cant, the answers to choose from are: 210 252 288 216 (my daughter circled 210)

Answer 252

kleenichols said:

Mom TRYING to check daughter's Pretest (didn't realize I had forgotten so much!) What is the easiest way to find the least common multiple of two numbers? This problem is: What is the least common multiple of 36 and 42...it is a multiple choice question, but I'd like to try to figure it out myself (just in case I cant, the answers to choose from are: 210 252 288 216 (my daughter circled 210)

Click to expand...

Here's a method that always works.

First, write the prime factorization of each number:

36 = 2[sup:38lugh6w]2[/sup:38lugh6w] * 3[sup:38lugh6w]2[/sup:38lugh6w]
42 = 2 * 3 * 7

Form the least common multiple by writing the product of all of the DIFFERENT factors that appear in the prime factorizations, using each one to the HIGHEST power it appears.

The different factors are 2, 3, and 7. The highest power of 2 is 2[sup:38lugh6w]2[/sup:38lugh6w] and the highest power of 3 is 3[sup:38lugh6w]2[/sup:38lugh6w]

So, the least common multiple is 2[sup:38lugh6w]2[/sup:38lugh6w] * 3[sup:38lugh6w]2[/sup:38lugh6w] * 7

Which IS 252, as Aladdin stated. BUT now you know how to get it.