61.8k views
1 vote
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?

User Vucalur
by
7.6k points

1 Answer

7 votes

Answer:

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.

User Dhruv Kapatel
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories