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The largest number of 4 digits exactly divisible by 12, 15, 18 and 27 is
- a)9720
- b)1000
- c)9270
- d)9999
Correct answer is 'A'. Can you explain this answer?
Verified Answer
The largest number of 4 digits exactly divisible by 12, 15, 18 and 27 ...
LCM (12, 15, 18, 27) = 540
Now, largest four digit number = 9999
∴ 9999 ÷ 540 = 18 x 540 + 279 (Remainder = 279) Therefore, the largest number of 4 digits exactly divisible by 12, 15, 18 and 27 is 9999 – 279 = 9720
Now, largest four digit number = 9999
∴ 9999 ÷ 540 = 18 x 540 + 279 (Remainder = 279) Therefore, the largest number of 4 digits exactly divisible by 12, 15, 18 and 27 is 9999 – 279 = 9720
Most Upvoted Answer
The largest number of 4 digits exactly divisible by 12, 15, 18 and 27 ...
Explanation:
Finding the LCM of 12, 15, 18, and 27:
- The LCM of 12, 15, 18, and 27 can be found by finding the prime factorization of each number.
- Prime factorization:
- 12 = 2 * 2 * 3
- 15 = 3 * 5
- 18 = 2 * 3 * 3
- 27 = 3 * 3 * 3
- The LCM is the product of the highest power of all prime factors involved:
- LCM = 2^2 * 3^3 * 5 = 4 * 27 * 5 = 540
Dividing 9999 by the LCM:
- To find the largest 4-digit number divisible by 12, 15, 18, and 27, we divide 9999 by the LCM:
- 9999 ÷ 540 = 18.5
Finding the largest number:
- To find the largest number less than or equal to 9999 that is divisible by the LCM (540), we multiply 540 by 18:
- 540 * 18 = 9720
Therefore, the largest number of 4 digits exactly divisible by 12, 15, 18, and 27 is 9720.
Finding the LCM of 12, 15, 18, and 27:
- The LCM of 12, 15, 18, and 27 can be found by finding the prime factorization of each number.
- Prime factorization:
- 12 = 2 * 2 * 3
- 15 = 3 * 5
- 18 = 2 * 3 * 3
- 27 = 3 * 3 * 3
- The LCM is the product of the highest power of all prime factors involved:
- LCM = 2^2 * 3^3 * 5 = 4 * 27 * 5 = 540
Dividing 9999 by the LCM:
- To find the largest 4-digit number divisible by 12, 15, 18, and 27, we divide 9999 by the LCM:
- 9999 ÷ 540 = 18.5
Finding the largest number:
- To find the largest number less than or equal to 9999 that is divisible by the LCM (540), we multiply 540 by 18:
- 540 * 18 = 9720
Therefore, the largest number of 4 digits exactly divisible by 12, 15, 18, and 27 is 9720.
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The largest number of 4 digits exactly divisible by 12, 15, 18 and 27 ...
A because 9720 is divisible with given numbers
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