When a number is divided by 12, 15, and 20, it leaves remainders 5, 8, and 13 respectively. What is the least such number?
Show answer & explanation
Correct answer: B
Explanation
When N is divided by 12, the remainder is 5.
When N is divided by 15, the remainder is 8.
When N is divided by 20, the remainder is 13.
N − 5 is divisible by 12.
N − 8 is divisible by 15.
N − 13 is divisible by 20.
N − 5 = 12k
N − 8 = 15m
N − 13 = 20n
5 = 12 − 7
8 = 15 − 7
13 = 20 − 7
N + 7 will be completely divisible by 12, 15, and 20.
12 = 2² × 3
15 = 3 × 5
20 = 2² × 5
LCM = 2² × 3 × 5 = 60
N + 7 = 60
N = 53