# math

posted by .

What is the lowest numberthat has a remainder of 1 when divided by 2 and a remainder of 2 when devided by 3 and a
remainder of 3 when divided by 4 and a remainder of 4 when divided by 5?

The answer is 59. There is a general method for solving such problms, but in this case you can use this trick. First, note that you don't have to demand that the remainder is 1 when divided by 2 becuse that follows from the fact that the remainder is 3 when divided by 4.

The number 60 is the product of 3, 4, and 5. All the remainders for 60 are thus zero and 60 is the smallest positive number with this property. Now, all the remainders of 60 + x are equal to x. But if x is equal or larger than y then the remainder after division by y is obtained by subtracting y until the number becomes less than y. In case x is negative you have to add y as many times to make the number equal or larger to zero.

If we take x equal to -1, then all the remainders are -1 plus the number you are dividing with, so it's one less than the number, which is exactly what we want.

## Similar Questions

1. ### Math - repost for Anonymous

Can someone show me the steps to these questions (I will provide the correct answers)?
2. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
3. ### math

what is the least common positive integer that meets the following conditions: divided by 7 with remainder 4 divided by 8 with remainder 5 divided by 9 with remainder 6 i thought you could add 7 and 4 to get 13, then divide 13 and …
4. ### Math

Find the least positive integer that leaves the remainder 3 when divided by 7, remainder 4 when divided by 9, and remainder 8 when divided by 11. Using the Chinese Remainder Theorem.
5. ### Math

How many integers bewteen 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
6. ### Math

How many integers between 200 and 500 inclusive leave a remainder 1 when divided by 7 and a remainder 3 when divided by 4?
7. ### Math

Find the smallest positive integer that leaves a remainder of 5 when divided by 7, a remainder of 6 when divided by 11, and a remainder of 4 when divided by 13.
8. ### math

When a is divided by 7,the remainder is 4.When b is divided by 3,the remainder is 2.If 0<a<24 and 2<b<8, which of the following could have a remainder of 0 when divided by 8?
9. ### math

1.) when the expression 4x^2-3x-8 is divided by x-a, the remainder is 2. find the value of a. 2.) the polynomial 3x^3+mx^2+nx+5 leaves a remainder of 128 when divided by x-3 and a remainder of 4 when divided by x+1. calculate the remainder …