Question

A basket of mangoes is packed into small boxes which can contain 38, 42 and 54 mangoes respectively. Find the minimum number of mangoes in the basket.

Answer 1

we should find the h.c.f and the answer will be 2

Answer 2

Given:

A basket of mangoes is packed into small boxes which can contain 38, 42 and 54 mangoes respectively.

To find:

Find the minimum number of mangoes in the basket.

Solution:

From the given information, we have the data as follows.

The minimum number of mangoes in the basket is equal to the LCM of 38, 42 and 54 mangoes.

From the given information, we have the data as follows.

Prime Factorization of 38 is:  2 × 19  ⇒  2¹  × 19¹

Prime Factorization of 42 is:  2 × 3 × 7  =>  2¹  × 3¹  × 7¹

Prime Factorization of 54 is:  2 × 3 × 3 × 3 =>  2¹ × 3³

Therefore, the LCM of 38, 42 and 54 is calculated as follows.

LCM = 2¹  × 3³ × 7¹ × 19¹  = 7182

Therefore, the minimum number of mangoes in the basket is 7182.