What is the sum of digits of the least number which when divided by 18, 24 and…
2019
What is the sum of digits of the least number which when divided by 18, 24 and 30 leaves the same remainder 8 in each case and is divisible by 19?
- A.
26
- B.
18
- C.
20
- D.
24
Attempted by 77 students.
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Correct answer: A
If 𝑁≡8(mod 18, 24, 30), then N−8 is a multiple of LCM(18,24,30)=360. So N=360k+8. For divisibility by 19: 360k+8≡0(mod19)⇒18k+8≡0⇒k≡8. Thus N=360×8+8=2888; digit sum =2+8+8+8=26.