Question

find HCF of 378,180 and 420 by prime factorization method. Is HCF x LCM of three numbers equal to the product of the three numbers .
Please answer the question fully.

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Answer 1

Answer:

Prime factors of 378 = 2 × 3 × 3 × 3 × 7

Prime factors of 180 = 2 × 2 × 3 × 3 × 5

Prime factors of 420 = 2 × 2 × 3 × 5 × 7

So, HCF of 378, 180 and 420 is 2 × 3 = 6

And LCM of 378, 180 and 420 is 2 × 2 × 3 × 3 × 3 × 5 × 7 = 3780

So, let us check whether LCM (378, 180 and 420) × HCF (378, 180 and 420) is equal to the product of the three numbers

3780 × 6 = 378 × 180 × 420

22680 ≠ 28576800

Hence LCM*HCF is not equal to the product of the three numbers.