Question

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

Answer 1

We have : $6=2^1\times 3^{1}and20=2\times 2\times 5=2^2\times 5^1$.
You can find HCF(6, 20) = 2 and $LCM(6,20)=2\times 2\times 3\times 5=60$, 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) = $2^2$ $\times$ 3 $\times$ 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) $\times$ LCM(6, 20) = 6 $\times$ 20. In fact, we can verify that for any two positive integers a and b, $HCF(a,b)\times LCM(a,b)=a\times b$. 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.