Which one of the following is the largest 3-digit number which when divided by 12, 15 and 18 respectively, gives a remainder 5 in each case ?

To find the largest 3-digit number that leaves a remainder of 5 when divided by 12, 15, and 18, we first calculate the Least Common Multiple (LCM) of the divisors:

• 12 = 2² × 3
• 15 = 3 × 5
• 18 = 2 × 3²

The LCM is 2² × 3² × 5 = 4 × 9 × 5 = 180. Any number satisfying the condition is of the form (180 × k) + 5, where k is an integer. To find the largest 3-digit number, we find the largest k such that 180k + 5 < 1000.

Testing values for k:
If k = 5: (180 × 5) + 5 = 900 + 5 = 905.
If k = 6: (180 × 6) + 5 = 1080 + 5 = 1085 (which is a 4-digit number).

Therefore, 905 is the largest 3-digit number that satisfies the given condition.