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Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder?
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Find the smallest number, which when divided by 4,12,1 and 20 leaves n...
Understanding the Problem
To find the smallest number that leaves no remainder when divided by 4, 12, 1, and 20, we need to determine the least common multiple (LCM) of these numbers.
Step 1: Identify the Factors
- The prime factorization of each number is as follows:
- 4 = 2²
- 12 = 2² × 3
- 1 = 1 (does not affect LCM)
- 20 = 2² × 5
Step 2: Determine the LCM
- To find the LCM, take the highest power of each prime factor from the factorizations:
- The highest power of 2 is 2².
- The highest power of 3 is 3¹.
- The highest power of 5 is 5¹.
Step 3: Calculate the LCM
- Now, multiply these together:
- LCM = 2² × 3¹ × 5¹
- LCM = 4 × 3 × 5
- LCM = 12 × 5
- LCM = 60
Final Result
- The smallest number that, when divided by 4, 12, 1, and 20, leaves no remainder is 60.
Conclusion
- Therefore, 60 is the least common multiple of the given numbers, making it the smallest number satisfying the condition.
To find the smallest number that leaves no remainder when divided by 4, 12, 1, and 20, we need to determine the least common multiple (LCM) of these numbers.
Step 1: Identify the Factors
- The prime factorization of each number is as follows:
- 4 = 2²
- 12 = 2² × 3
- 1 = 1 (does not affect LCM)
- 20 = 2² × 5
Step 2: Determine the LCM
- To find the LCM, take the highest power of each prime factor from the factorizations:
- The highest power of 2 is 2².
- The highest power of 3 is 3¹.
- The highest power of 5 is 5¹.
Step 3: Calculate the LCM
- Now, multiply these together:
- LCM = 2² × 3¹ × 5¹
- LCM = 4 × 3 × 5
- LCM = 12 × 5
- LCM = 60
Final Result
- The smallest number that, when divided by 4, 12, 1, and 20, leaves no remainder is 60.
Conclusion
- Therefore, 60 is the least common multiple of the given numbers, making it the smallest number satisfying the condition.
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Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder?
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Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder?.
Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number, which when divided by 4,12,1 and 20 leaves no reminder?.
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