How To Find the LCM of Numbers By Alisa Bengen

Mr. Jones, Mr. Banks, and Mr. Mercey are long-time old friends. They all go to the races. Mr. Jones goes every 10 days. Mr. Banks goes to the races every 50 days. Mr. Mercey goes every 25 days. If they saw each other there, when is the next time they will see each other if they continue to go in this pattern? Real-Life Problem

We are going to start this the hardest way first: finding all the multiples of the numbers. 10 {10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150} 50 {50, 100, 150, 200, 250, 300, 350, 400, 450, 500} 25 {25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275} What numbers are a multiple that all the numbers have? There are 50, 100, and 150. So which one is the LCM? The smallest number, of course. So Mr. Jones, Mr. Banks and Mr. Mercey will see each other at the races every 50 days. Doing the Math: Finding Multiples

You can figure this problem out by doing a “factor tree,” also known as prime factorization. You take each number and lay it out. Then, you figure out which numbers go into them. You underline the prime numbers to make it easier. Then, you see which numbers match. You can eliminate 1 of these matching numbers. Then, you multiply all of the primes that are left, not counting the big numbers. Remember to leave out the eliminated numbers! Doing the Math: Using Primes x 5 5 x 10 2 x 5 5 x 5 5 x 2 x 5= 50, or the LCM of 10, 50 and (5 x 2= 10 x 5= 50)

The least common multiple is 50. Therefore, Mr. Jones, Mr. Banks and Mr. Mercey will see each other every 50 days at the races. Also, remember for smaller numbers, it is easier to find their multiples, like this: 6 {6, 12 …} and for bigger numbers, it is easier to use a “factor tree” then multiply the primes. Solution