Find the difference between the greatest and the smallest 4-digit numbers exactly divisible by 36 and 48.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 8928.
LCM of 36 and 48 = 144
The smallest 4-digit number divisible by 144
⇒ 1000/144 = 6.94 (approximately), so the next whole number is 7
The smallest 4-digit number divisible by 144 = 7 × 144 = 1008
The greatest 4-digit number divisible by 144
⇒ 9999/144 = 69.44 (approximately), so the whole number is 69
The greatest 4-digit number divisible by 144 = 69 × 144 = 9936
Hence,
The difference between the greatest and smallest 4-digit numbers divisible by 144 = 9936 - 1008 = 8928