Least Common Multiple

Least common multiple of two numbers is the smallest number (not zero) that is a multiple of both. To do this you use prime factorization. For example, take the numbers 30 and 45. The prime factorization of these two numbers are:

30= 2 x 3 x 5

45= 3 x 3 x 5 

Then multiply the factors the greatest number of times it shows up in either number. Sometimes the factor occurs more than once in both numbers, you then multiply the factor the greatest number of times it occurs.

For 30 and 45 you will multiply: 2 x 3 x 3 x 5=90. The reason the 3 is multiplied twice is because it occurs twice in one prime factorization. The other numbers only occur once. So the least common multiple of 30 and 45 is 90. You can check your work by then dividing 90 by both 30 and 45.

90/45=2                               90/30=3

This verifies that 90 can be divided evenly by 45 and 30.

Another example!

What is the least common multiple of 12 and 80?

To find the solution you need to do prime factorization.

12= 2 x 2 x 3

80= 2 x 2 x 2 x 2 x 5

Since 2 occurs 4 times in the prime factorization of 80 you need to multiply it 4 times. The 3 and 5 are multiplied once each.

So you would multiply: 2 x 2 x 2 x 2 x 3 x 5=240

The least common multiply of 12 and 80 is 240. To verify this you divide 240 by 80 and 12 to see if can be divided evenly.

240/12=20                         240/80=3

240 is the least common multiply of 12 and 80!

https://www.youtube.com/watch?v=D6yHKOYJiso