The hcf of 2472, 1284 and a third number ‘n’ is 12. If their lcm is 2^3 × 3^2 × 5 × 103 × 107, then the number ‘n’ is:

Given,

HCF of 2472, 1284 and a third number ‘n’ is 12.

Their LCM is 23 × 32 × 5 × 103 × 107

Prime factorisation of 2472 = 2 × 2 × 2 × 3 × 103  = 23 × 3 × 103

Prime factorisation of 1284 = 2 × 2 × 3 × 107 = 22 × 3 × 107

HCF (2472, 1284) = 2 × 2 × 3 = 2× 3

Thus, n also has the factors 2× 3

From the LCM of three numbers, the another factor as the missing element of other number, i.e., 3 × 5

Therefore,

n = 2× 3 × 3 × 5

n = 180

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