Question

Prove that a*b=LCM*HCF

Answer 1

Consider two numbers say 15 and 36. Their factors are

15 = 3x5

36 = 2x2x3x3

So HCF = 3 and LCM = 2x2x3x3x5 = 180

The product of HCF and LCM = 2x2x3x3x3x5 = 540.

See the product of the numbers themselves: 15x36 = 540.

Conclusion: The product of the HCF and LCM of two numbers is the same as the product of the numbers themselves.