Question #99831

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Answer 1 · 2017-12-19T02:26:06

The LCM is #80#

Factor each number:

#16 = 2*2*2*2 = 2^4#

#20 = 2*2*5=2^2*5#

Every multiple of #16# has factors that include #2^4#

Every multiple of #20# has factors that include #2^2*5#.

The Least Common Multiple must include factors of #2^4#, #2^2# and #5# and no extra factors (otherwise it wouldn't be "least")

The least number that includes these is #2^4*5 = 80#

Answer 2 · 2017-12-19T08:28:57

#LCM = 2xx2xx2xx2xx5 = 80#

The LCM must be divisible by #16 and 20#

Write each number as the product of its prime factors:

#" "16 =2xx2xx2xx2#
#" "ul(20= 2xx2color(white)(xxxxxx)xx5)#
#LCM = 2xx2xx2xx2xx5 = 80#

#80# now contains all the factors of #16 and 20# but without any duplicates,