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22 vote

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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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 :
1). 289
2). 391
3). 221
4). 731

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2 answers

26 vote
Answered by on | Votes 26 | | Last Updated: 2021-11-28 06:48:38

221

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36 vote
Answered by on | Votes 36 |
Let the numbers be 17x and 17y where x and y are co-prime. LCM of 17x and 17y = 17 xy According to the question, 17xy = 714 xy =$\frac{714}{17}$ = 42= 6x7 x = 6 and y = 7 or, x = 7 and y =6. First number = 17x = 17 × 6 = 102 Second number = 17y =17 × 7 = 119 Sum of the numbers = 102 + 119 = 221




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