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We need to find the least common multiple of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. We can find the least common multiple of smaller sets of numbers, and then compare those least common multiples.

Any number is a multiple of 1, so we do not need to consider it further.

The least common multiple of 2, 4, and 8 is 8, since 8 is a multiple of both 2 and 4.

The least common multiple of 3 and 9 is 9, since 9 is a multiple of 3.

The least common multiple of 5 and 10 is 10, since 10 is a multiple of 5.

So, now we have reduced the set of numbers to 6, 7, 8, 9, and 10.

To determine the least common multiple of more than two numbers, we can take them two at a time, then compare those least common multiples to find their least common multiple. To determine the least common multiple of two numbers, determine the prime factors of both numbers. Then, determine the prime factors they have in common. Multiply all their prime factors together (in other words, multiply both numbers together) and divide by the prime factors they have in common (in other words, their greatest common factor).

The least common multiple of 6 and 7 is 42, since their greatest common factor is 1.

The least common multiple of 8 and 9 is 72, since their greatest common factor is 1.

So, now we have reduced the set of numbers to 10, 42, and 72.

The greatest common factor of 10 and 42 is 2, so the least common multiple is 10 x 42 Ã· 2 = 210.

Now, we only need to determine the least common multiple of 72 and 210.

First, determine the greatest common factor of both numbers.

The prime factors of 72 are 2, 2, 2, 3, and 3.

The prime factors of 210 are 2, 3, 5, and 7.

The prime factors they have in common are 2 and 3, so the greatest common factor is 2 x 3 = 6.

The least common multiple of 72 and 210 is 72 x 210 Ã· 6 = 2520.

Doublecheck:

2520 Ã· 10 = 252 = 22 x 32 x 7

2520 Ã· 9 = 280 = 22 x 5 x 7

2520 Ã· 8 = 315 = 32 x 5 x 7

2520 Ã· 7 = 360 = 23 x 32 x 5

2520 Ã· 6 = 420

2520 Ã· 5 = 504

2520 Ã· 4 = 630

2520 Ã· 3 = 840

2520 Ã· 2 = 1260

2520 Ã· 1 = 2520

From the prime factorization of the first four division results above, you can see that they do not have a prime factor common to all, which confirms that we have the least common multiple.

LCM for 10, 9, 8, 7, 6, 5, 4, 3, 2, and 1 is 2520, which is the multiple of the highest power of prime factors in the given numbers (23 x 32 x 5 x 7).

Q: What is the least common multiple of the numbers from 1 to 10?

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There is not a least common multiple of a single number, such as 10, because there cannot be a least common multiple without two or more numbers to compare. Common multiples are multiples that the numbers being compared have in common. The least common multiple is the smallest multiple that all the numbers being compared have in common.Examples:The least common multiple of 8 and 10 is 40.The least common multiple of 10 and 35 is 70.The least common multiple of 10 and 43 is 430.The least common multiple of 3, 10, and 66 is 330.You need to provide two or more positive integer numbers to properly answer this.

The LCM of 3 and 10 is 30.The least common multiple of two numbers is the product of the two numbers divided by their greatest common factor. The greatest common factor of 3 and 10 is 1. So, the least common multiple is 3 x 10 Ã· 1 = 30.30

The numbers are 5 and 10.

10 and 20, among others.

The LCM of 8, 9, and 10 is 360. 8 = 2^3 9 = 3^2 10 = 5 x 2 The least common multiple is therefore 2^3 x 3^2 x 5 = 360

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The least common multiple of the numbers 5 and 10 is 10.

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The least common multiple of the numbers 7 and 10 is 70.

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The least common multiple of the numbers 10 and 24 is 120.

The Least Common Multiple (LCM) for 10 11 is 110.

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There is not a least common multiple of a single number, such as 10, because there cannot be a least common multiple without two or more numbers to compare. Common multiples are multiples that the numbers being compared have in common. The least common multiple is the smallest multiple that all the numbers being compared have in common.Examples:The least common multiple of 8 and 10 is 40.The least common multiple of 10 and 35 is 70.The least common multiple of 10 and 43 is 430.The least common multiple of 3, 10, and 66 is 330.You need to provide two or more positive integer numbers to properly answer this.

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