Find the least number which when divided by 20, 25, 35, and 40 leaves remainders 14, 19, 29, and 34 respectively.
Show answer & explanation
Correct answer: A
Explanation
Given:
Numbers = 20, 25, 35, 40
Remainder = 14, 19, 29, 34
Formula:
If N is divided by a, then r is the remainder, then
N − r is exactly divisible by that number.
N − 14 is divisible by 20
N − 19 is divisible by 25
N − 29 is divisible by 35
N − 34 is divisible by 40
20 − 14 = 6
25 − 19 = 6
35 − 29 = 6
40 − 34 = 6
Therefore,
N + 6 is exactly divisible by 20, 25, 35, and 40.
LCM (20, 25, 35, 40)
20 = 2² × 5
25 = 5²
35 = 5 × 7
40 = 2³ × 5
LCM = 2³ × 5² × 7 = = 1400
N + 6 = 1400
N = 1394
Smallest number = 1394