Question

The HCF of two numbers is 4 and their LCM is 400. How many pairs of values can the numbers assume?

Answer 1

HCF of two numbers is 4
So, the numbers can be 4a and 4b.
Now, 4a × 4b = 4 × 400
⇒ ab = 100
So, we can get the pairs
a = 25 and b = 4
a = 4 and b = 25
Thus, the numbers are 4 × 25 = 100 and 4 × 4 = 16.
Also, we can get the other pair 4 × 1 = 4 and 400.
Hence, there are two pairs.