How To Find the LCM of
Numbers
By Alisa Bengen
Real-Life Problem
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?
Doing the Math: Using Primes
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!
10
50
25
2x5
5 x 10
5x5
10
5 x 2 x 5= 50, or the LCM of 10, 50 and 25.
(5 x 2= 10 x 5= 50)
2x5
Solution
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.