What is the least number which when divided by 12, 16, 18 and 30 leaves a…
2023
What is the least number which when divided by 12, 16, 18 and 30 leaves a remainder of 4 in each case but is completely divisible by 7?
Answer: D. 2884 — LCM of 12, 16, 18, and 30 is 720. The required number is of the form 720k + 4. For divisibility by 7: 720k + 4 ≡ 0 (mod 7). Since 720 ≡ 6, 6k + 4 ≡ 0, giving…
- A.
4245
- B.
4242
- C.
2324
- D.
2884
Attempted by 241 students.
Show answer & explanation
Correct answer: D
LCM of 12, 16, 18, and 30 is 720.
The required number is of the form 720k + 4.
For divisibility by 7: 720k + 4 ≡ 0 (mod 7). Since 720 ≡ 6, 6k + 4 ≡ 0, giving k ≡ 4 (mod 7).
For k = 4, the least number is 720 x 4 + 4 = 2884.
Loading lesson…