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The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
- a)10
- b)100
- c)504
- d)2520
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The least number that is divisible by all the numbers from 1 to 10 (bo...
The least number divisible by all the numbers from 1 to 10 will be the LCM of these numbers.
We have,
1 = 1
2 = 2 * 1
3 = 3 * 1
4 = 2 * 2
5 = 5 * 1
6 = 2 * 3
7 = 7 * 1
8 = 2 * 2 * 2
9 = 3 * 3
10 = 2 * 5
So, LCM of these numbers = 1 * 2 * 2 * 2 * 3 * 3 * 5 * 7 = 2520
Hence, least number divisible by all the numbers from 1 to 10 is 2520
Most Upvoted Answer
The least number that is divisible by all the numbers from 1 to 10 (bo...
The least number divisible by all the numbers from 1 to 10 will be the LCM of these numbers.
We have,
1 = 1
2 = 2 × 1
3 = 3 × 1
4 = 2 × 2
5 = 5 × 1
6 = 2 × 3
7 = 7 × 1
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
So, LCM of these numbers = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520
Hence, least number divisible by all the numbers from 1 to 10 is 2520.
We have,
1 = 1
2 = 2 × 1
3 = 3 × 1
4 = 2 × 2
5 = 5 × 1
6 = 2 × 3
7 = 7 × 1
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
So, LCM of these numbers = 1 × 2 × 2 × 2 × 3 × 3 × 5 × 7 = 2520
Hence, least number divisible by all the numbers from 1 to 10 is 2520.
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Community Answer
The least number that is divisible by all the numbers from 1 to 10 (bo...
The least number that is divisible by all the numbers from 1 to 10 can be found by finding the least common multiple (LCM) of these numbers. LCM is the smallest multiple that is divisible by all the given numbers.
To find the LCM of the numbers from 1 to 10, we need to list the prime factors of each number and then take the highest power of each prime factor.
Let's break down the numbers from 1 to 10 and find their prime factors:
1 = 1
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2 × 3
7 = 7
8 = 2^3
9 = 3^2
10 = 2 × 5
Now let's take the highest power of each prime factor:
2^3, 3^2, 5, 7
To find the LCM, we multiply these prime factors together:
LCM = 2^3 × 3^2 × 5 × 7
Now let's simplify this expression:
LCM = 8 × 9 × 5 × 7
LCM = 5040
Therefore, the least number that is divisible by all the numbers from 1 to 10 is 5040.
Therefore, the correct answer is option C) 504.
To find the LCM of the numbers from 1 to 10, we need to list the prime factors of each number and then take the highest power of each prime factor.
Let's break down the numbers from 1 to 10 and find their prime factors:
1 = 1
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2 × 3
7 = 7
8 = 2^3
9 = 3^2
10 = 2 × 5
Now let's take the highest power of each prime factor:
2^3, 3^2, 5, 7
To find the LCM, we multiply these prime factors together:
LCM = 2^3 × 3^2 × 5 × 7
Now let's simplify this expression:
LCM = 8 × 9 × 5 × 7
LCM = 5040
Therefore, the least number that is divisible by all the numbers from 1 to 10 is 5040.
Therefore, the correct answer is option C) 504.
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The least number that is divisible by all the numbers from 1 to 10 (both inclusive) isa)10b)100c)504d)2520Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The least number that is divisible by all the numbers from 1 to 10 (both inclusive) isa)10b)100c)504d)2520Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The least number that is divisible by all the numbers from 1 to 10 (both inclusive) isa)10b)100c)504d)2520Correct answer is option 'D'. Can you explain this answer?.
The least number that is divisible by all the numbers from 1 to 10 (both inclusive) isa)10b)100c)504d)2520Correct answer is option 'D'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The least number that is divisible by all the numbers from 1 to 10 (both inclusive) isa)10b)100c)504d)2520Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The least number that is divisible by all the numbers from 1 to 10 (both inclusive) isa)10b)100c)504d)2520Correct answer is option 'D'. Can you explain this answer?.
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