the greatest 4 digit number such that when it divided by 15, 18,21,and 24,it leaves remainder 5 in each case is
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What is the greatest 4-digit number, that when it divided by 15, 18, 21, and 24, will leave a remember of 5 in each case?
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3 Answers

Adarsh, Math & Computer Science Nerd
Answered January 24, 2018 · Author has 192 answers and 558.7K answer views
Thanks for A2A.
The LCM of 15, 18, 21 and 24 is 2520.
So the only positive integers that will leave remainder 5 when divided by all of those is 5 more than a multiple of 2520.
Such a number would be of the form 2520n+5.
1000 ≦ 2520n+5 ≦ 9999
Subtract 4 from all three sides:
995 ≦ 2520n ≦ 9994
Divide all three sides by 2520:
0.3948… ≦ n ≦ 3.9658…
Since n is an integer: 1 ≦ n ≦ 3
So the smallest such 4 digit number is when n=1, 2520*1 + 5 = 2525.
And the greatest such 4 digit number is when n=3, 2520*3 + 5 = 7565