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Find the least number which when divided by 12, 15, 18, 20 and 24 leaving remainder 5 each time
- a)365
- b)360
- c)245
- d)185
Correct answer is option 'A'. Can you explain this answer?
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Find the least number which when divided by 12, 15, 18, 20 and 24 leav...
Explanation:
Finding the Least Common Multiple (LCM):
- In order to find the least number which when divided by 12, 15, 18, 20, and 24 leaving a remainder of 5 each time, we need to find the least common multiple (LCM) of these numbers.
- LCM of 12, 15, 18, 20, and 24 can be calculated by finding the prime factors of each number and taking the highest power of each prime factor.
Calculating LCM:
- Prime factors of each number:
- 12 = 2^2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
- 20 = 2^2 * 5
- 24 = 2^3 * 3
- Taking the highest power of each prime factor:
- LCM = 2^3 * 3^2 * 5 = 360
Finding the Required Number:
- When a number is divided by the LCM (360) and leaves a remainder of 5 each time, the least number satisfying this condition is given by LCM + 5.
- Therefore, the required number = 360 + 5 = 365
Therefore, the correct answer is option 'A' - 365.
Finding the Least Common Multiple (LCM):
- In order to find the least number which when divided by 12, 15, 18, 20, and 24 leaving a remainder of 5 each time, we need to find the least common multiple (LCM) of these numbers.
- LCM of 12, 15, 18, 20, and 24 can be calculated by finding the prime factors of each number and taking the highest power of each prime factor.
Calculating LCM:
- Prime factors of each number:
- 12 = 2^2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
- 20 = 2^2 * 5
- 24 = 2^3 * 3
- Taking the highest power of each prime factor:
- LCM = 2^3 * 3^2 * 5 = 360
Finding the Required Number:
- When a number is divided by the LCM (360) and leaves a remainder of 5 each time, the least number satisfying this condition is given by LCM + 5.
- Therefore, the required number = 360 + 5 = 365
Therefore, the correct answer is option 'A' - 365.
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Find the least number which when divided by 12, 15, 18, 20 and 24 leaving remainder 5 each timea)365b)360c)245d)185Correct answer is option 'A'. Can you explain this answer?
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