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

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Answer 1 · 2016-09-04T22:07:03

144

#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

Answer 2 · 2016-09-05T15:38:06

#144#

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#