Question
Both the H.C.F and the difference of two numbers is 7. If the L.C.M of the two numbers is a three digit number, then what is the maximum possible value of the smaller number?
Answer: Option A
:
A
Let the smaller number be 7x, then the larger number will be (7x+7) = 7(x+1)
Since x and (x+1) are co-prime, the LCM would be 7×x×(x+1).
Maximum value of x such that LCM is a three digit number is x=11.
So, smaller number = 77.
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:
A
Let the smaller number be 7x, then the larger number will be (7x+7) = 7(x+1)
Since x and (x+1) are co-prime, the LCM would be 7×x×(x+1).
Maximum value of x such that LCM is a three digit number is x=11.
So, smaller number = 77.
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