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Find the smallest number that is multiple of all the numbers from 1 to 10?
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Find the smallest number that is multiple of all the numbers from 1 to...
Understanding the Problem
To find the smallest number that is a multiple of all the numbers from 1 to 10, we need to determine the Least Common Multiple (LCM) of these numbers. The LCM is the smallest number that each of the numbers can divide without leaving a remainder.
Step 1: Identify the Numbers
The numbers we need to consider are:
Step 2: Find Prime Factorizations
Next, we find the prime factorization of each number:
Step 3: Determine Maximum Powers
To find the LCM, we take the highest power of each prime factor present:
Step 4: Calculate the LCM
Now, multiply these maximum powers together:
LCM = 2³ × 3² × 5¹ × 7¹
Calculating that:
Final Calculation
Now multiply these together:
Conclusion
Thus, the smallest number that is a multiple of all the numbers from 1 to 10 is 2520.
To find the smallest number that is a multiple of all the numbers from 1 to 10, we need to determine the Least Common Multiple (LCM) of these numbers. The LCM is the smallest number that each of the numbers can divide without leaving a remainder.
Step 1: Identify the Numbers
The numbers we need to consider are:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
Step 2: Find Prime Factorizations
Next, we find the prime factorization of each number:
- 1 = 1
- 2 = 2
- 3 = 3
- 4 = 2²
- 5 = 5
- 6 = 2 × 3
- 7 = 7
- 8 = 2³
- 9 = 3²
- 10 = 2 × 5
Step 3: Determine Maximum Powers
To find the LCM, we take the highest power of each prime factor present:
- 2: 2³ (from 8)
- 3: 3² (from 9)
- 5: 5¹ (from 5 or 10)
- 7: 7¹ (from 7)
Step 4: Calculate the LCM
Now, multiply these maximum powers together:
LCM = 2³ × 3² × 5¹ × 7¹
Calculating that:
- 2³ = 8
- 3² = 9
- 5¹ = 5
- 7¹ = 7
Final Calculation
Now multiply these together:
- 8 × 9 = 72
- 72 × 5 = 360
- 360 × 7 = 2520
Conclusion
Thus, the smallest number that is a multiple of all the numbers from 1 to 10 is 2520.
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Find the smallest number that is multiple of all the numbers from 1 to 10? 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 multiple of all the numbers from 1 to 10? 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 multiple of all the numbers from 1 to 10?.
Find the smallest number that is multiple of all the numbers from 1 to 10? 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 multiple of all the numbers from 1 to 10? 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 multiple of all the numbers from 1 to 10?.
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