SOLUTION: When a certain number is divided by 2, there is a remainder of 1. When the same number is divided by 3, 4 and 5, there are remainders of 2, 3, and 4 respectively. What is the smal

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Question 990538: When a certain number is divided by 2, there is a remainder of 1. When the same number is divided by 3, 4 and 5, there are remainders of 2, 3, and 4 respectively. What is the smallest positive number for which the conditions are satisfied?
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
Let the number be n.

n = 1 mod 2
n = 2 mod 3
n = 3 mod 4
n = 4 mod 5

The smallest value of n is 1 less than the LCM of 2, 3, 4, and 5, which is 59.
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.

If you add 1 to the number, you will get the number multiple of 2, 3, 4, 5.


The smallest such a number is  LCM(2,3,4,5) = 60.


THEREFORE, the number under the problem's question is  60-1 = 59.    ANSWER

Solved.



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