Question

Find the HCF and LCM of 6, 72 and 120 using the prime factorisation method. [3 MARKS]

Answer 1

Prime factorisation : 1 Mark
H.C.F : 1 Mark
L.C.M : 1 Mark

We have :

$6=2\times 3$,

$72=2^3\times 3^2$,

$120=2^3\times 3\times 5$

Here, $2^1$ and $3^1$ are the smallest powers of the common factors 2 and 3 respectively.

So, HCF (6, 72, 120) $=2^1\times 3^1=2\times 3=6$

Also, $2^3$, $3^2$ and $5^1$ are the greatest powers of the prime factors 2, 3 and 5 respectively involved in the three numbers.

So, LCM (6, 72, 120) $=2^3\times 3^2\times 5^1=360$