Question #99831

2 Answers
Dec 19, 2017

The LCM is 80

Explanation:

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

Dec 19, 2017

LCM = 2xx2xx2xx2xx5 = 80

Explanation:

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,