If an integer n is divisible by 3, 5 and 12, what is the next larger integer…
2024
If an integer n is divisible by 3, 5 and 12, what is the next larger integer divisible by all these numbers?
- A.
n + 20
- B.
n + 40
- C.
n + 30
- D.
n + 60
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Correct answer: D
Key idea: Find the least common multiple (LCM) of 3, 5, and 12.
Compute prime factorizations: 3 = 3, 5 = 5, 12 = 2^2 × 3.
Take the highest powers of primes: 2^2, 3, and 5. So LCM = 2^2 × 3 × 5 = 60.
Since n is divisible by all three numbers, n = 60k for some integer k. The next larger integer divisible by all three is (k + 1) × 60 = n + 60.
Answer: n + 60