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Question

Find the LCM and HCF of 6 and 20 by the prime factorisation method.

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Solution

We have : 6=21×31and20=2×2×5=22×51.
You can find HCF(6, 20) = 2 and LCM(6,20)=2×2×3×5=60, as done in your earlier classes.
Note that HCF(6, 20) = 2 = Product of the smallest power of each common prime factor in the numbers.
LCM (6, 20) = 22 × 3 × 5 = Product of the greatest power of each prime factor, involved in the numbers.
From the example above, you might have noticed that HCF(6, 20) × LCM(6, 20) = 6 × 20. In fact, we can verify that for any two positive integers a and b, HCF(a,b)×LCM(a,b)=a×b. We can use this result to find the LCM of two positive integers, if we have already found the HCF of the two positive integers.


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