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I have been searching in vain for a general proof of the following:

a*b = LCM(a,b)*HCF(a,b)

Please send me a link of please give me the proof. Or at least, please help me visualize how this comes about... I know it is true... but I'm just not able to visualize it...

I go up to seeing the product of the two numbers as the product of their respective prime factors and that contains the HCF of the Two numbers. But, I'm unable to visualize the rest of the prime factors together becoming the LCM of the two numbers.... please help me...

Thank you.

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# A*b = LCM(a,b)*HCF(a,b)

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