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Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7?
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Find the smallest number that is the multiple of all the numbers from ...
To find the smallest number that is a multiple of all the numbers from 1 to 10, excluding 7, we need to determine the least common multiple (LCM) of the numbers: 1, 2, 3, 4, 5, 6, 8, 9, and 10.
Step 1: List the Numbers
- 1
- 2
- 3
- 4
- 5
- 6
- 8
- 9
- 10
Step 2: Prime Factorization
- 1 = (no prime factors)
- 2 = 2
- 3 = 3
- 4 = 2²
- 5 = 5
- 6 = 2 × 3
- 8 = 2³
- 9 = 3²
- 10 = 2 × 5
Step 3: Determine the Highest Powers
To find the LCM, take the highest power of each prime number from the factorizations:
- 2: The highest power is 2³ (from 8)
- 3: The highest power is 3² (from 9)
- 5: The highest power is 5¹ (from 5)
Step 4: Calculate the LCM
Now, multiply these highest powers together:
- LCM = 2³ × 3² × 5¹
- LCM = 8 × 9 × 5
Calculating step-by-step:
- 8 × 9 = 72
- 72 × 5 = 360
Final Answer
The smallest number that is a multiple of all the numbers from 1 to 10, excluding 7, is:
- 360
Step 1: List the Numbers
- 1
- 2
- 3
- 4
- 5
- 6
- 8
- 9
- 10
Step 2: Prime Factorization
- 1 = (no prime factors)
- 2 = 2
- 3 = 3
- 4 = 2²
- 5 = 5
- 6 = 2 × 3
- 8 = 2³
- 9 = 3²
- 10 = 2 × 5
Step 3: Determine the Highest Powers
To find the LCM, take the highest power of each prime number from the factorizations:
- 2: The highest power is 2³ (from 8)
- 3: The highest power is 3² (from 9)
- 5: The highest power is 5¹ (from 5)
Step 4: Calculate the LCM
Now, multiply these highest powers together:
- LCM = 2³ × 3² × 5¹
- LCM = 8 × 9 × 5
Calculating step-by-step:
- 8 × 9 = 72
- 72 × 5 = 360
Final Answer
The smallest number that is a multiple of all the numbers from 1 to 10, excluding 7, is:
- 360
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Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7?.
Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7? for Class 6 2024 is part of Class 6 preparation. The Question and answers have been prepared according to the Class 6 exam syllabus. Information about Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7? covers all topics & solutions for Class 6 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the smallest number that is the multiple of all the numbers from 1 to 10 except for 7?.
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