In mathematics, the least common multiple, or lowest common denominator (abbreviated LCD), of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, LCM(a, 0) is typically undefined. However, some authors define LCM(a, 0) as a, which is the LCM of a and 0 if a is nonzero. The LCM of a and b is written as LCM(a, b), LCM[a, b], lcm(a, b), or sometimes just as a · b.
The LCM of more than two integers is called the least common multiple or the lowest common denominator. For example, the LCM of 3 and 4 is 12. The LCM of 6 and 10 is 30. The LCM of more than two integers is not necessarily unique. For example, the LCM of 3, 4, and 6 is 12. Other examples are given below.
The concept of least common multiple can be extended to other commensurable objects, such as polynomials, ideals in a ring, subgroups of a group, etc.
Take a look at this: What Is the Lcm of 4 and 10?
What is the smallest number that is a multiple of both 6 and 10?
The smallest number that is a multiple of both 6 and 10 is 30. 30 is a multiple of 6 because it is evenly divisible by 6 (30/6 = 5). 30 is a multiple of 10 because it is evenly divisible by 10 (30/10 = 3). Therefore, the smallest number that is a multiple of both 6 and 10 is 30.
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What is the LCM of 6 and 10?
The LCM of 6 and 10 is 30.
The LCM (lowest common multiple) is the smallest positive integer that is a multiple of two or more numbers. In other words, it is the smallest number that can be evenly divided by all of the numbers in question.
To find the LCM of 6 and 10, we can list the multiples of each number until we find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 Multiples of 10: 10, 20, 30, 40, 50, 60
As we can see, 30 is the first number that appears on both lists. Therefore, 30 is the LCM of 6 and 10.
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Frequently Asked Questions
What is least common multiple (lcm) of 6 and 10?
LCM (6,10) = 30
How do you find the least common multiple of two numbers?
The least common multiple of two numbers is the number that can be divided evenly by both and represents the smallest number that contains both numbers. In this example, 60 represents the least common multiple of 6 and 10.
What is the full form of LCM?
The full form of the least common multiple is: LCM = (n×m) / (n+m)
How do you find the LCM of 6 and 10?
In order to find the LCM of 6 and 10, we need to multiply the highest exponent prime factors. The highest exponent prime factor for 6 is 3 and for 10 it is 5. Therefore, theLCM of 6 and 10 is 16.
What is least common multiple multiple (LCM)?
In mathematics, the least common multiple of two numbers is the largest number that can be divided evenly by both numbers without leaving a remainder. For instance, 26 is the LCM of 3 and 5 because it can be divided evenly by 3 and 5 without leaving a remainder (3 ÷ 5 = 1).
Sources
- https://www.cuemath.com/numbers/lcm-of-6-and-10/
- https://gcflcm.org/lcm-of-6-and-10
- https://answers.everydaycalculation.com/lcm/6-10
- https://byjus.com/maths/lcm-of-6-and-10/
- https://socratic.org/questions/how-do-you-find-the-least-common-multiple-of-6-and-10
- https://math.answers.com/basic-math/What_is_the_smallest_number_that_is_a_multiple_of_two_or_more_numbers_called
- https://math.answers.com/Q/What_are_common_multiples_of_6_and_10
- https://rikeinvest.com/en/math/sansu/kobaisu/sk6and10/
- https://math.answers.com/other-math/What_is_the_least_common_multiple_of_6_and_10
- https://studystoph.com/math/question8786946
- https://profound-answers.com/what-is-the-smallest-multiple-other-than-zero-that-two-or-more-numbers-have-in-common/
- https://math.answers.com/other-math/What_is_the_smallest_multiple_of_any_number
- https://mathbig.com/all-lcm-of-pages/lcm-of-6-and-10
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