Question

find lcm and hcf by prime factorization method 72 and 108​

Answer 1

Answer:

36

Step-by-step explanation:

$72 = 36 \times 2 = 18 \times 2 \times 2 = 9 \times 2 \times 2 \times 2 = 3 \times 3 \times 2 \times 2 \times 2$

$108 = 54 \times 2 = 27 \times 2 \times 2 = 3 \times 3 \times 3 \times 2 \times 2$

HCF=3×3×2×2=36

Better Method :

HCF(108,72) :

$108 = 72 \times 1 + 36$

$72 = 36 \times 2 + 0$

We can clearly see that remainder is 0, Hence 36 is the HCF. This method is called Euclids division lemma

Answer 2

Answer:

Prime factorisation of 72=2×2×2×3×3

Prime factorisation of 108=2×2×3×3×3

HCF=2×2×3×3=36

LCM=2×2×2×3×3×3=216

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