*least common multiple*(LCM) of two or more numbers is the smallest number (not zero) that's a multiple of both or all the numbers. Finding the LCM is a useful technique for solving many problems on the ASVAB AFQT math subtests—especially those involving fractions.

One way to find the LCM is to list the multiples of each number, one at a time, until you find the smallest multiple that's common to all the numbers.

Try the following example: find the LCM of 45 and 50.

**Multiples of 45:**45, 90, 135, 180, 225, 270, 315, 360, 405, 450**Multiples of 50:**50, 100, 150, 200, 250, 300, 350, 400, 450

That's rather cumbersome, isn't it? Wouldn't it be great if you had an easier way? Fortunately, you do: An easier way to find the LCM is first to list the prime factors of each number:

- The prime factors for 45 are
- The prime factors for 50 are

Here's one more example: what is the least common multiple of 5, 27, and 30?

List the prime factors of each number:

**Prime factors of 5:**5

**Prime factors of 27:**

**Prime factors of 30:**

The number 3 occurs a maximum of three times, 5 occurs a maximum of one time, and 2 occurs a maximum of one time:

Check your answer by seeing whether 5, 27, and 30 can all divide evenly into 270.