Question

Find the lcm of the following set of number using decomposition method.
8,16 and 24 =lcm=

Answer 1

48

Explanation:

`\mathrm{The\:LCM\:of\:}a,\:b\mathrm{\:is\:the\:smallest\:positive\:number\:that\:is\:divisible\:by\:both\:}a\mathrm{\:and\:}b`

LCM of 8, 16 and 24

Decompose to prime factors
8/2 = 4; 4/2 = 2. So 8 = 2 x 2 x 2

16 = 8 x 2 = (2 x 2 x 2) x 2

24 = 8 x 3 = (2 x 2 x 2) x 3

2 x 2 x 2 is common, 2 appears once more as a factor in 16 and 3 appears in 24 so the LCM = (2 x 2 x 2) x 2 x 3 = 48