Find the largest number of four digits such that on dividing by 15, 18, 21 and 24 the remainders are 11, 14, 17 and 20 respectively.

Solution(By Examveda Team)

LCM of (15, 18, 21, 24)
⇒ 5 × 3 × 6 × 7 × 4 = 2520
⇒ In such type of questions,we take the difference between given number and remainder of that number.
Number Remainder
⇒ (15 - 11) = 4
⇒ (18 - 14) = 4
⇒ (21 - 17) = 4
⇒ (24 - 20) = 4
      It will be same always
Now, Largest 4 digit number is 9999
⇒ On dividing 9999 by LCM (2520) we get remainder
⇒ 2439
Subtract remainder from 9999 we get largest 4 digit number, which is divisible by given number
= 9999 - 2439 = 7560 (9999 but required number gives difference on dividing)
So, our required number = 7560 - 4(difference) = 7556