About Least Common Multiple
LCM is an abbreviation for "Least Common Multiple." The smallest number that can be divided by both numbers is called the least common multiple of two numbers. It can be calculated with two or more numbers or fractions.
There are several ways to calculate the LCM of two numbers. One of the quickest approaches to get the LCM of two numbers is to utilise the prime factorization of each number, then multiply the product of the highest powers of the common prime factors.
What do you mean by Least Common Multiple (LCM)?
In mathematics, the least common multiple is referred to as LCM (or) the lowest common multiple. The smallest number among all common multiples of two or more numbers is called the least common multiple. Take two integers, for example, 2 and 5. Each set of multiples will be unique. 2’s multiples are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, …..…
5’s multiples are 5, 10, 15, 20, …..…
The typical multiples of 2 and 5 are thus 10, 20,..... The number 10 is the smallest among the numbers 10, 20,... Thus, 10 is the least common multiple of 2 and 5. LCM (2, 5) = 10 is one way to write it.
Finding LCM
Different approaches can be used to determine the LCM of numbers. To find the least common multiple of two numbers, there are three approaches.
- LCM by using Listing Method
- LCM by using Prime Factorization
- LCM by using Division Method
- LCM by using Listing Method
We may identify the common multiples of two or more numbers by using the listing out the frequent multiples method. The least common multiple is chosen among these frequent multiples, and the LCM of two numbers can therefore be determined. Follow the steps below to find the LCM of the two numbers A and B using the listing method:
Step 1: Write down the first few A and B multiples.
Step 2: Make a list of the frequent multiples of both integers.
Select the least common multiple in step three. The LCM of the two numbers is the lowest common multiple.
LCM using Prime Factorization
We can discover the prime factors of numbers using the prime factorization method, and then use those prime factors to find the LCM of those numbers. Follow the steps below to find the LCM of two numbers using the prime factorization method:
Step 1: Write the numbers in prime factorization form.
Step 2: The product of all prime factors is the LCM of the given two numbers. (Common factors, on the other hand, will only be mentioned once.)
LCM by using Division Method
We divide the numbers by a common prime number using the division method, and the prime factors are utilised to determine the LCM of those numbers. Follow the steps below to find the LCM of two numbers using the division method:
Step 1: Determine a prime number that is a factor of at least one of the numbers given. To the left of the provided numbers, write this prime number.
Step 2: Divide the number by the prime number in step 1 and write the quotient below if the prime number is a factor of the number. If the prime number in step 1 is not a factor of the number, leave it blank in the row below. Continue until only one step remains in the last row. LCM Formula for Integers
If a and b are both integers, the formula for finding their least common multiple is: (a x b)/HCF = LCM (a,b) (a,b)
Fractions and the LCM Formula
If the two fractions are a/b and c/d, the formula for their least common multiple is
LCM (a/b, c/d) = (LCM of Numerators)/(HCF of Denominators) = LCM (a,c)/HCF (a,c) (b,d)
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