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Question

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

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Solution

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

We have :

6=2×3,

72=23×32,

120=23×3×5

Here, 21 and 31 are the smallest powers of the common factors 2 and 3 respectively.

So, HCF (6, 72, 120) =21×31=2×3=6

Also, 23, 32 and 51 are the greatest powers of the prime factors 2, 3 and 5 respectively involved in the three numbers.

So, LCM (6, 72, 120) =23×32×51=360


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