When 12, 15, 18, 20 and 25 divide the least number x, the remainder in each case was 3 but x was divisible by 7. What is the value of x?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 903
Let the number be x
When divided by 12, 15, 18, 20, 25, remainder = 3 → x − 3 divisible by 12, 15, 18, 20, 25
LCM of 12, 15, 18, 20, 25 = 22 × 32 × 52 = 900
x − 3 = 900k → x = 900k + 3
x divisible by 7 → 900k + 3 ≡ 0 mod 7
900 mod 7 = 4 → 4k + 3 ≡ 0 mod 7
4k ≡ 4 mod 7 → k = 1
x = 900 × 1 + 3 = 903