In mathematics, the least common multiple, also known as the lowest common denominator (LCD), of two integers a and b, usually denoted as LCM(a, b), is the smallest positive integer that is divisible by both a and b.
For example, LCM(4, 10) = 20 because 20 is the smallest positive integer that is divisible by both 4 and 10.
The LCM of more than two integers is also well-defined: it is the smallest positive integer that is divisible by each of them.
LCM(4, 10, 15) = 60 because 60 is the smallest positive integer that is divisible by all of 4, 10, and 15.
The least common multiple is a natural number that is assigned to a set of numbers to indicate how often the numbers in the set go into one another evenly. It is the smallest number that all of the numbers in the set will go into evenly.
The method of finding the least common multiple of two numbers is different than finding the greatest common factor. The LCM is the smallest number that is a multiple of both numbers while the GCF is the greatest number that is a factor of both numbers. To find the LCM, list the multiples of each number until a common multiple is found.
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What is the greatest common divisor of 4 and 10?
The greatest common divisor of 4 and 10 is 2. There are a few different ways to find the greatest common divisor of two numbers. One way is to list the factors of each number and then find the largest number that appears on both lists. The factors of 4 are 1, 2, and 4, while the factors of 10 are 1, 2, 5, and 10. The greatest common divisor is 2.
Another way to find the greatest common divisor is to use a division algorithm. To do this, divide the larger number by the smaller number and then continue to divide the remainder by the last number until you get a remainder of 0. Using this method, we would divide 10 by 4 to get 2 with a remainder of 2. We would then divide 4 by 2 to get 2 with a remainder of 0, which means that 2 is the greatest common divisor.
The greatest common divisor is important because it can be used to simplify fractions. For example, the greatest common divisor of 4 and 10 is 2, so we can simplify the fraction 4/10 by dividing both the numerator and denominator by 2 to get 2/5. This is just one example of how the greatest common divisor can be used in real life.
Discover more: What Is the Lcm of 2 and 8?
What is the highest common factor of 4 and 10?
There is no definitive answer to this question as it depends on how you define "highest common factor". If you are simply looking for the largest number that divides evenly into both 4 and 10, then the answer is 2. However, if you are looking for the largest number that is a factor of both 4 and 10, then the answer is 4.
Related reading: What Is the Sum of a Number and 4?
What is the smallest number that is a multiple of both 4 and 10?
What is the smallest number that is a multiple of both 4 and 10?
The smallest number that is a multiple of both 4 and 10 is 20.
20 is the smallest number that is a multiple of both 4 and 10 because it is the smallest number that is evenly divisible by both 4 and 10. To find the smallest number that is a multiple of both 4 and 10, we can use the least common multiple (LCM).
The LCM of 4 and 10 is 20.
The LCM is the smallest number that is a multiple of both 4 and 10.
To find the LCM of 4 and 10, we can use the prime factorization method.
The prime factorization of 4 is 2 x 2.
The prime factorization of 10 is 2 x 5.
When we find the LCM of 4 and 10, we multiply the highest exponent of each prime number.
2 x 2 x 5 = 20
Therefore, the LCM of 4 and 10 is 20.
The smallest number that is a multiple of both 4 and 10 is 20.
What is the largest number that is a multiple of both 4 and 10?
There is no largest number that is a multiple of both 4 and 10. This is because there is no limit to the number of times that 4 and 10 can be multiplied together. For example, 40 is a multiple of both 4 and 10, and so is 400. Therefore, we can say that the largest number that is a multiple of both 4 and 10 is infinity.
What is the smallest positive integer that is a multiple of both 4 and 10?
What is the smallest positive integer that is a multiple of both 4 and 10?
The number 4 is a multiple of 2, and the number 10 is a multiple of 5. Therefore, the smallest positive integer that is a multiple of both 4 and 10 is 20.
What is the largest positive integer that is a multiple of both 4 and 10?
Assuming you are asking for the largest positive integer that is a multiple of both 4 and 10, the answer would be 40. 40 is the largest positive integer that is a multiple of both 4 (it is divisible by 4) and 10 (it is divisible by 10).
Related reading: Common Multiple
What is the product of the lowest common multiple and the greatest common divisor of 4 and 10?
The product of the lowest common multiple and the greatest common divisor of 4 and 10 is 40. The lowest common multiple of 4 and 10 is 20, and the greatest common divisor of 4 and 10 is 2. Therefore, the product of the lowest common multiple and the greatest common divisor of 4 and 10 is 40.
What is the product of the highest common factor and the smallest positive integer that is a multiple of both 4 and 10?
The product of the highest common factor and the smallest positive integer that is a multiple of both 4 and 10 is 40.
Frequently Asked Questions
What is the smallest multiple of 3 and 5?
15
What is the least common multiple of 4 and 5?
20
What is the least common multiple of two numbers?
To find the least common multiple of two numbers, divide both numbers by the LCM. For example, if you are dividing 24 by LCM (4,6), the answer would be 12.
What are the multiples of 4?
4,8,12,16,20,24,28,32,36,40
What is a multiple of 5 and 2?
5 is a multiple of 2 because 5 × 1 = 5, so 5 is also a multiple of 2. 10 is the smallest positive integer that is divisible by both 5 and 2, so it is the least common multiple of 5 and 2.
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