The greatest four-digit number that is divisible by each of the numbers 12, 18, 21, and 28 is?
Show answer & explanation
Correct answer: C
Explanation
Given:
Maximum four-digit number = 9999
Numbers = 12, 18, 21, 28
12 = 2² × 3
18 = 2 × 3²
21 = 3 × 7
28 = 2² × 7
LCM = 2² × 3² × 7 = 252
Now the largest multiple of 252 less than or equal to 9999 is
9999 ÷ 252 = 39 (remainder)
252 × 39 = 9828