Question

What number divided by 6 leaves a remainder of 5, divided by 5 leaves a remainder of 4, divided by 4 leaves a remainder of 3, and divided by 3 leaves a remainder of 2?

Answer 1

59

Explanation:

If a number is divided by
`n` and leaves a remainder
`(n-1)`, then the number
`(n+1)` will be completely divisible by
`n`.

Therefore, when we say a number
`x`, when divided by 6, it leaves a remainder 5, then (
`x+1`) will be a multiple of 6.

When we say a number
`x`, when divided by 5, it leaves a remainder 4, then (
`x+1`) will be a multiple of 5.

When we say a number
`x`, when divided by 4, it leaves a remainder 3, then (
`x+1`) will be a multiple of 4.

When we say a number
`x`, when divided by 3, it leaves a remainder 2, then (
`x+1`) will be a multiple of 3.

So,
`x+1` is a common multiple of 3, 4, 5 and 6.

Taking LCM of 3, 4, 5 and 6, we get 60.

So, the number 60 - 1 = 59 is the least such number.