Question
Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.
✓
Answer
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, $\operatorname{HCF}(6,72,120)=2^{1 \times} 3^1=2^{\times} 3=6$
$2^3, 3^2$ and $5^1$ are the greatest powers of prime factors 2,3 and 5 respectively involved in the three numbers.
So, $\operatorname{LCM}(6,72,120)=2^{3 \times} 3^{2 \times} 5^1=360$
Here, $2^1$ and $3^1$ are the smallest powers of the common factors 2 and 3 respectively.
So, $\operatorname{HCF}(6,72,120)=2^{1 \times} 3^1=2^{\times} 3=6$
$2^3, 3^2$ and $5^1$ are the greatest powers of prime factors 2,3 and 5 respectively involved in the three numbers.
So, $\operatorname{LCM}(6,72,120)=2^{3 \times} 3^{2 \times} 5^1=360$
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