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If an integer n is divisible by 3, 5 and 12, what is the next larger integer divisible by all these numbers?
- a)n + 3
- b)n + 5
- c)n + 12
- d)n + 60
- e)n + 15
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If an integer n is divisible by 3, 5 and 12, what is the next larger i...
If n is divisible by 3, 5 and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60.
n = 60 k
n + 60 is also divisible by 60 since
n + 60 = 60 k + 60 = 60(k + 1)
The answer is D.
n = 60 k
n + 60 is also divisible by 60 since
n + 60 = 60 k + 60 = 60(k + 1)
The answer is D.
Most Upvoted Answer
If an integer n is divisible by 3, 5 and 12, what is the next larger i...
Next Larger Integer Divisible by 3, 5, and 12
To find the next larger integer that is divisible by 3, 5, and 12, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest multiple that is divisible by all the given numbers.
Step 1: Find the prime factorization of each number
- The prime factorization of 3 is 3.
- The prime factorization of 5 is 5.
- The prime factorization of 12 is 2 * 2 * 3.
Step 2: Find the highest power of each prime factor
- The highest power of 2 is 2 * 2 = 4.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor
- Multiply the highest power of 2, 3, and 5: 4 * 3 * 5 = 60.
Therefore, the next larger integer divisible by 3, 5, and 12 is 60.
Explanation:
- By finding the LCM of 3, 5, and 12, we ensure that the resulting number is divisible by all three numbers.
- The LCM is calculated by finding the highest power of each prime factor that appears in the prime factorization of the given numbers and multiplying them together.
- In this case, the highest power of 2 is 2 * 2 = 4, the highest power of 3 is 3, and the highest power of 5 is 5. Multiplying these highest powers gives us 4 * 3 * 5 = 60, which is the next larger integer divisible by 3, 5, and 12.
- Option D, n = 60, is the correct answer.
To find the next larger integer that is divisible by 3, 5, and 12, we need to find the least common multiple (LCM) of these three numbers. The LCM is the smallest multiple that is divisible by all the given numbers.
Step 1: Find the prime factorization of each number
- The prime factorization of 3 is 3.
- The prime factorization of 5 is 5.
- The prime factorization of 12 is 2 * 2 * 3.
Step 2: Find the highest power of each prime factor
- The highest power of 2 is 2 * 2 = 4.
- The highest power of 3 is 3.
- The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor
- Multiply the highest power of 2, 3, and 5: 4 * 3 * 5 = 60.
Therefore, the next larger integer divisible by 3, 5, and 12 is 60.
Explanation:
- By finding the LCM of 3, 5, and 12, we ensure that the resulting number is divisible by all three numbers.
- The LCM is calculated by finding the highest power of each prime factor that appears in the prime factorization of the given numbers and multiplying them together.
- In this case, the highest power of 2 is 2 * 2 = 4, the highest power of 3 is 3, and the highest power of 5 is 5. Multiplying these highest powers gives us 4 * 3 * 5 = 60, which is the next larger integer divisible by 3, 5, and 12.
- Option D, n = 60, is the correct answer.
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If an integer n is divisible by 3, 5 and 12, what is the next larger integer divisible by all these numbers?a)n + 3b)n + 5c)n + 12d)n + 60e)n + 15Correct answer is option 'D'. Can you explain this answer?
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