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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.
Therefore, we must have
Thus, the two numbers are 20 and 28., and so the smaller number is 20.
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