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The H.C.F. of two numbers, each having three digits , is 17 and their L.C.M. is 714. The sum of the numbers will be :
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- 289
- 391
- 221
- 731
Correct Option: C
Let the numbers be 17p and 17q where p and q are co-prime. LCM of 17p and 17q = 17pq
According to the question ,
17pq = 714
| ⇒ pq = | = 42 = 6 × 7 | |
| 17 |
⇒ p = 6 and q = 7
or, p = 7 and q =6.
∴ First number = 17p = 17 × 6 = 102
Second number = 17q = 17 × 7 = 119
∴ Sum of the numbers = 102 + 119 = 221
