Prove that a*b=LCM*HCF
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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.
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