SOLUTION: Find the greatest number of 5 digits which when divided by 25,30,40 leaves a remainder of 20,25 and 35 respectively?

Question 1090941: Find the greatest number of 5 digits which when divided by 25,30,40 leaves a remainder of 20,25 and 35 respectively?
Answer by ikleyn(52812) (Show Source): You can put this solution on YOUR website!
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Find the greatest number of 5 digits which when divided by 25,30,40 leaves a remainder of 20,25 and 35 respectively?
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Let N be the number under the question.

Let us consider the number N+5.


Then, according to the condition, the number N+5 leaves the remainders 25, 30 and 40 when divided by 25, 30 and 40, respectively.


It is the same as to say that the number N+5 leaves the remainder 0 when divided by 25, 30 and 40.


The least common multiple (LCM) of the numbers 25, 30 and 40 is 600.


 = 1666.67,


therefore, the number N+5 is equal to 1666*600 = 999600.


Then the number N under the question is 999600-5 = 999595.

Solved.

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