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#
