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(52810)   (Show Source):
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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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