# What is the least common multiple of #{120, 130, 144}?

##### 1 Answer

May 18, 2016

#### Explanation:

Let us start by finding the prime factorisations of each of the numbers:

#120 = 2 xx 2 xx 2 xx 3 xx 5#

#130 = 2 xx 5 xx 13#

#144 = 2 xx 2 xx 2 xx 2 xx 3 xx 3#

So the smallest number that contains all of these factors in these multiplicities is:

#2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 5 xx 13 = 9360#

If you don't have a calculator to hand, an easier way to do that last multiplication might be:

#2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 5 xx 13#

#=13 xx (3 xx 3) xx 2 xx 2 xx 2 xx (2 xx 5)#

#=13 xx 9 xx 2 xx 2 xx 2 xx 10#

#=13 xx (10 - 1) xx 2 xx 2 xx 2 xx 10#

#=(130 - 13) xx 2 xx 2 xx 2 xx 10#

#=(117 xx 2) xx 2 xx 2 xx 10#

#=(234 xx 2) xx 2 xx 10#

#=(468 xx 2) xx 10#

#=936 xx 10#

#=9360#