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Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.?
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Find the smallest number that is a multiple of all the numbers from 1 ...
To find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7, we need to determine the least common multiple (LCM) of the remaining numbers: 1, 2, 3, 4, 5, 6, 8, 9, and 10.
Step 1: Prime Factorization
- The prime factorization of each number is as follows:
- 1 = 1
- 2 = 2
- 3 = 3
- 4 = 2²
- 5 = 5
- 6 = 2 × 3
- 8 = 2³
- 9 = 3²
- 10 = 2 × 5
Step 2: Identify Maximum Powers
- For the LCM, take the highest power of each prime number:
- Prime 2: Max power is 2³ (from 8)
- Prime 3: Max power is 3² (from 9)
- Prime 5: Max power is 5¹ (from 5)
Step 3: Calculate the LCM
- Now, multiply these maximum powers together:
LCM = 2³ × 3² × 5¹
= 8 × 9 × 5
= 72 × 5
= 360
Conclusion
- Therefore, the smallest number that is a multiple of all the numbers from 1 to 10 except for 7 is 360.
Step 1: Prime Factorization
- The prime factorization of each number is as follows:
- 1 = 1
- 2 = 2
- 3 = 3
- 4 = 2²
- 5 = 5
- 6 = 2 × 3
- 8 = 2³
- 9 = 3²
- 10 = 2 × 5
Step 2: Identify Maximum Powers
- For the LCM, take the highest power of each prime number:
- Prime 2: Max power is 2³ (from 8)
- Prime 3: Max power is 3² (from 9)
- Prime 5: Max power is 5¹ (from 5)
Step 3: Calculate the LCM
- Now, multiply these maximum powers together:
LCM = 2³ × 3² × 5¹
= 8 × 9 × 5
= 72 × 5
= 360
Conclusion
- Therefore, the smallest number that is a multiple of all the numbers from 1 to 10 except for 7 is 360.
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Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.?
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Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.? 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 that is a multiple of all the numbers from 1 to 10 except for 7.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.?.
Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.? 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 that is a multiple of all the numbers from 1 to 10 except for 7.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number that is a multiple of all the numbers from 1 to 10 except for 7.?.
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