Question

What is the smallest number which when divided by 16, 20, and 25 leaves remainder 7, 11, and 16 respectively? M4maths

Answer 1

16 - 7 = 9

20 - 11 = 9

25 - 16 = 9

We observe that 9 is the common number.

LCM( 16,20,25) = 400

Smallest number = 400 - 9 = 391

Answer 2

Given,

When a number is divided by 16, 20, and 25 leaves remainder 7, 11, and 16 respectively

To Find,

The smallest number =?

Solution,

Let the number be n

LCM of (16 , 20 , 25) = 400

The number leaves a remainder when divided by 16 = 7

Difference = 16 - 7 = 9

The number leaves a remainder when divided by 20 = 11

Difference = 20 - 11 = 9

The number leaves a remainder when divided by 25 = 16

Difference = 25 - 16 = 9

Therefore, 9 is common is all this numbers as the difference.

Therefore,  n = LCM of (16 , 20 , 25)  - 9

n = 400 - 9

n = 391

Hence, the smallest number which when divided by 16, 20, and 25 leaves remainder 7, 11, and 16 respectively is 391.