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The ratio of the sum to the LCM of two natural numbers is 7 : 12. If their HCF is 4, then the smaller number is :
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- 20
- 16
- 12
- 8
Correct Option: C
Let the numbers be 4p and 4q where p and q are prime to each other.
LCM = 4pq
| ∴ | = | |||
| 4pq | 12 |
⇒ 12 (p + q) = 7pq
⇒ p = 3, q = 4
∴ Smaller number = 4 × 3 = 12
