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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 :
- A289
- B391
- C221
- D731
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CCommunity
221
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CCommunity
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
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