Find the sum of the numbers between 550 and 700 such that when they are divided by 12, 16 and 24, leave remainder 5 in each case.

Question: Find the sum of the numbers between 550 and 700 such that when they are divided by 12, 16 and 24, leave remainder 5 in each case.

Solution:
Given that,
The number between 550 and 700 such that when they are divided by 12, 16, and 24, leave the remainder 5 in each case.
∴ LCM of 12, 16, and 24 = 48

Multiple of 48 bigger than 550 which leaves remainder 5 are,
1st Number = 48 × 12 + 5 = 581
2nd Number = 48 × 13 + 5 = 629
3rd Number = 48 × 14 + 5 = 677

∴ Sum of these numbers are = 581 + 629 + 677 = 1887

Hence, The sum of the numbers are 1887.