In mathematics, the least common multiple, or lowest common multiple, of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is a multiple of both a and b. For example, LCM(3, 9) = 9 because the next smallest common multiple of 3 and 9 is 12. LCM(3, 9) is also written as 3 × 9 = 27, 30, 33, ....
The least common multiple is useful for solving many different types of math problems. For example, it can be used to find the least common denominator for two or more fractions. In this case, the LCM of 3 and 9 is 9, so the least common denominator of 2/3 and 1/9 is 9.
The LCM can also be used to solve problems involving multiplication. For instance, if two people each have 3 apples and 9 oranges, then the total number of fruit is 3 × 9 = 27.
In general, the least common multiple of two or more integers is the smallest positive integer that is a multiple of all of the integers. Therefore, to find the LCM of 3 and 9, one must first find all of the positive integer multiples of 3 and 9.
The positive integer multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, ...
The positive integer multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...
As seen in the lists above, the LCM of 3 and 9 is 9.
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What is the greatest common factor of 3 and 9?
There are a few methods that can be used to find the greatest common factor of 3 and 9. One method is to list the factors of each number. The factors of 3 are 1, 3. The factors of 9 are 1, 3, 9. The greatest common factor of 3 and 9 is 1.
Another method is to use the prime factorization of each number. The prime factorization of 3 is 3. The prime factorization of 9 is 3 x 3. The greatest common factor of 3 and 9 is 3.
One last method is to use the Euclidean algorithm. This algorithm can be used to find the greatest common factor of any two numbers. To use the Euclidean algorithm, start by finding the smaller number of the two and divide it into the larger number. In this case, divide 3 into 9. The answer is 3 with a remainder of 0. Since the remainder is 0, the greatest common factor of 3 and 9 is 3.
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What is the product of 3 and 9?
The product of 3 and 9 is 27.
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How can you find the least common multiple of 3 and 9?
To find the least common multiple of 3 and 9, we must first understand what a multiple is. A multiple is simply a number that is the product of two other numbers. So, 3 multiplied by 9 is a multiple of 3 and 9.
The least common multiple is the smallest multiple that two numbers have in common. In other words, it's the smallest number that is a multiple of both 3 and 9.
To find the least common multiple of 3 and 9, we can start by listing out the first few multiples of each number:
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
As we can see, the least common multiple of 3 and 9 is 9.
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What is the LCM of 3 and 9?
The least common multiple, or LCM, of 3 and 9 is 3 × 9 = 27.
The LCM is the smallest positive integer that is a multiple of both 3 and 9. In other words, the LCM is the smallest positive integer that is divisible by both 3 and 9.
The LCM of 3 and 9 is therefore 27.
Curious to learn more? Check out: What Is the Product of Any Integer and 1?
What is the smallest number that is a multiple of both 3 and 9?
What is the smallest number that is a multiple of both 3 and 9?
The smallest number that is a multiple of both 3 and 9 is 9.
9 is a multiple of 3 because it can be evenly divided by 3. 9 is also a multiple of 9 because it can be evenly divided by 9.
Since 9 is the smallest number that is a multiple of both 3 and 9, it is also the answer to the question.
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Frequently Asked Questions
What is the least common multiple (lcm) of 3 5 9?
LCM (3,5,9) = 45
How to find the least common multiple of 3 numbers?
To find the LCM of 3 numbers, enter the first two numbers in the field below and click on calculate. The result will appear in the next field. LCM of 2 Numbers: 16 LCM of 3 Numbers: 28
What are the multiples of 3 5 and 9?
3, 5 and 9 are the multiples of 3.
What is the least common multiple of 6 and 8?
6 and 8 have a least common multiple of 24.
What is the least common factor (LCM) of 3 5 6?
The least common factor of 3, 5 and 6 is 15.
Sources
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- https://www.calculatorsoup.com/calculators/math/gcf.php
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