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1. The HCF of 2472, 1284 and a third number 'N' is 12. If their LCM is 2³ × 3² × 5 × 103 × 107, then the number 'N' is:

A. 2² × 3² × 7

B. 2² × 3³ × 10

C. 2² × 3² × 5

D. None of these

Solution:

We have,
HCF of the numbers × LCM of the numbers = Multiplication of the numbers.
(12) × (2³ × 3² × 5 × 103 × 107) = 2472 × 1284 × N
Hence,
N =

\frac{{(12) \times (2^{3} \times 3^{2} \times 5 \times 103 \times 107)}}{2472 \times 1284}

Or, N = 3 × 5

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