Question

The GCD of two numbers is 17 and their LCM is 765. How many pairs of values can the numbers assume?
(a) 1 (b) 2 (c) 3 (d) 4

Answer 1

GCD of two numbers is 17
So, the numbers can be 17a and 17b.
Now, 17a × 17b = 17 × 765
⇒ ab = 45
So, we can get two pairs
a = 5 and b = 9 or a = 9 and b = 5
Thus, the numbers are 17 × 5 = 85 and 17 × 9 = 153.
Also, we can get the other pair 17 × 1 = 17 and 765.
Hence, the correct answer is option (b).