Question

the LCM of 9,12 and n is 252 n is odd find all the possible value of n

Answer 1

answer : 7, 21 and 63

explanation : first of all, find prime factors of 9, 12 and 252 .

prime factors of 9 = 3 × 3

prime factors of 12 = 2 × 2 × 3

prime factors of 252 = 2 × 2 × 3 × 3 × 7

it is given that LCM of 9, 12 and n is 252

neither of prime factors of them {9, 12} contains 7.

so, n must contain 7. it can also contain 2 and 3.

so, n = 7, 2 × 7 , 3 × 7, 2 × 3 × 7 , 2 × 2 × 7, 3 × 3 × 7

= 7, 14, 21, 28, 63

but n is odd so, n = 7, 21 and 63.