Question

A number has a remainder of 1 when divided by 4 a remainder of 2 when divided by 5 and a remainder of 3 when divided by 6. What is the smallest number that has the above properties?

Answer 1

Smallest number with the properties in the question = 57

Explanation:

Let's first find the LCM of the three numbers which it is divided by which are 4,5,6.

LCM of 4,5 and 6 is 60.

We are told that;

The number has a remainder of 1 when divided by 4

The number has a remainder of 2 when divided by 5

The number has a remainder of 3 when divided by 6

In all 3 cases, the difference between the divisor and the remainder is 3.

This means that the smallest number in that has the properties in the question must be; 60 - 3 = 57