The HCF of two numbers is 4 and the two other factors of LCM are 5 and 7. Find the smaller of the two numbers.

Given that the H.C.F. of two numbers is 4 and the other two factors of the L.C.M are 5 and 7.

We are to find the smaller of the two numbers.

Let a and b be the two numbers where a < b.

Since the L.C.M. has three factors 4, 5 and 7 and H.C.F. of a and b is 4.

So, 4 is a factor of both the numbers a and b.

Also, 5 is a factor of one number and 7 is a factor of the other number.

The two numbers will be 5*4 and 7*4.

Thus, the two numbers are 20 and 28., and so the smaller number is 20.