Find the LCM and HCF of the following integer by applying the pri… - Vidyadip

Question

Find the $LCM$ and $HCF$ of the following integer by applying the prime factorisation method.
$84, 90$ and $120$

✓

Answer

$84, 90$ and $120$
Prime factor of 84, 90 and 120 are,

$84 = 2 \times 2 \times 3 \times 7 = 2^2 \times 3 \times 7$

$90 = 2 \times 3 \times 3 \times 5 = 2 \times 3^2 \times 5$

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

For H.C.F:

Common prime factor	Least component
2	1
3	1

H.C.F $(84, 90, 120) = 2 × 3 = 6$
For L.C.M:

Prime factor of 84, 90, 120	Greatest component
2	3
3	2
5	1
7	1

$L.C.M (84, 90, 120) = 2^3 \times 3^2 \times 5 \times 7$
$= 72 \times 35$
$= 2520$
Thus, H.C.F = 6 and L.C.M = 2520

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