Question

The product of two numbers is 504. If their LCM is 84, find their HCF.

Answer 1

Answer:

Let's go into the prime factorization of 504:

2×252=504

2×126=252

2×63=126

3^2×7=63

So 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.

Answer 2

Answer:

84 X H. C.F divided by 504

84 X H. C. F/504 and the answer will be 6