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, $HCF$ $(6, 72, 120) = 2^1\times3^1= 2 \times 3 = 6$
$2^3, 3^2$ and $5^1$ are the greatest powers of prime factors $2, 3$ and $5$ respectively involved in the three numbers.
So, $LCM$ $(6, 72, 120) = 2^3 \times 3^2 \times 5^1= 360$
Here, $2^1$ and $3^1$ are the smallest powers of the common factors $2$ and $3$ respectively.
So, $HCF$ $(6, 72, 120) = 2^1\times3^1= 2 \times 3 = 6$
$2^3, 3^2$ and $5^1$ are the greatest powers of prime factors $2, 3$ and $5$ respectively involved in the three numbers.
So, $LCM$ $(6, 72, 120) = 2^3 \times 3^2 \times 5^1= 360$
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