Question

The sum and lcm of two no is 156 and 504. Find both the number?

Answer 1

the prime factorization of 504 is:

2^3×3^2×7

Now looking at 156:

156=13×12

So, we have two numbers, 12a, and 12b, that add up to 504, or a and b that add up to 13.

a and b must be factors of 504, but we know certain rules: they must use all unused factors in 504 not in 12, so they must use 2,3, and 7.

7 multiplied by any other of the prime factors is greater than 13 so one of a or b must be 7. That makes the other 6, both because 2×3=6 and because 13–7=6.

That makes our numbers 72 and 84.