Question
Find the LCM and HCF of the following integer by applying the prime factorisation method.
$84, 90$ and $120$
$84, 90$ and $120$
✓
Answer
$84, 90$ and $120$
Prime factor of $84, 90$ and $120$ are,
For H.C.F:
H.C.F $(84, 90, 120) = 2 \times 3 = 6$
For L.C.M:
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 $= 2520$
Prime factor of $84, 90$ and $120$ are,
$84 = 2 \times 2 \times 3 \times 7 = 2^2 \times 3 \times 7$
$90 = 2 \times 3 \times 3 \times 5 = 2 \times 3^2 \times 5$
$120 = 2 \times 2 \times 2 \times 3 \times 5 = 2^3 \times 3 \times 5$
|
Common prime factor
|
Least component
|
|
$2$
|
$1$
|
|
$3$
|
$1$
|
For L.C.M:
|
Prime factor of $84, 90, 120$
|
Greatest component
|
|
$2$
|
$3$
|
|
$3$
|
$2$
|
|
$5$
|
$1$
|
|
$7$
|
$1$
|
$= 72 \times 35$
$= 2520$
Thus, H.C.F = 6 and L.C.M $= 2520$
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