Question

10. The greatest 4 digit number, such that when it divided by 15, 18, 21 and 24, it leaves remainder 5 in
ench case is
(1) 7565
(2) 7556
(3) 5756
(4) 6575
​

Answer 1

Answer:

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.

Step-by-step explanation:

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