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