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
Answer: d
Explanation: HCF of the numbers × LCM of the numbers = Multiplication of the numbers.
(12) × (23 × 32 × 5 × 103 × 107) = 2472 × 1284 × N
Hence,
N = $$\frac{{\{ \left( {12} \right) \times \left( {{2^3} \times {3^2} \times 5 \times 103 \times 107} \right)\} }}{{2472 \times 1284}}$$
N = 3 × 5
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