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

Answer:

59

Step-by-step 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.