What is the least common multiple of the set of numbers 8, 12, 16, 36?

2 Answers
Sep 4, 2016

144

Explanation:

8=2^3
12=2^2*3
16=2^4
36=2^2*3^2
So the lowest common multiple must be 2^4*3^2
Or 144

Sep 5, 2016

144

Explanation:

The first thing to notice is that:
8 is a factor of 16 and
12 is a factor of 36.

Therefore we do not need to consider 8 and 12 at all,

Find the LCM of 16 and 36.

Find the product of their prime factors.

color(white)(xxxxxx)16 = 2xx2xx2xx2 color(white)(xxxxxx)= 2^4
color(white)(xxxxxx)36 = 2xx2color(white)(xxxxxx)xx3xx3 = 2^2 xx3^2

LCM = color(white)(..xx)= 2xx2xx2xx2 xx3xx3 = 2^4 xx 3^2 =144

A multiple of 16 must include 2^4
A multiple of 36 must include 2^2 and 3^2

The LCM must have the highest of each, hence 2^4 xx 3^2