Question

Find

(a)the largest integer which is a factor of 96 and 294

(b) The smallest positive integer
n for ehich 96n is a multiple of 294

Answer 1

(a) 6

(b) 49

Explanation:

(a) The largest integer which is a factor of 96 and 294 should be their HCF.

Therefore, 96 = 2 × 2 × 2 × 2 × 2 × 3

294 = 2 × 3 × 7 × 7

Therefore, HCF = 2 × 3 = 6

(b) 96n should be the LCM of 96 and 294.

We know, product of two numbers = HCF × LCM

or, LCM = (96 × 294)/6 = 4704

So, 96n = 4704

or n = 49

Hope it helps.

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