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?

• A. 77
• B. 84
• C. 70
• D. 63

Answer 1

The correct option is A

77

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 $7\times x\times (x+1)$.

Maximum value of x such that LCM is a three digit number is x=11.

So, smaller number = 77.