LCM formula steps and solved examples for two or more numbers
We first need to understand what is LCM (Least common multiple)? Why is it used? It is the lowest number that is completely divisible by each of the given numbers. LCM stands for "Least Common Multiple" which is the smallest positive integer that is a multiple of two or more integers added together. We can find the L.C.M of two or more numbers using three methods. In this article, we will dive into the basics of the LCM method and understand how to find LCM and represent it.
Full Form of LCM
How to Find LCM by Listing Method
We can find out the common multiples of two or more numbers. Out of these repeated multiples, the LCM of two numbers can be calculated.
Steps to calculate LCM by listing method:
List the initial range of each number's multiples.
Search for multiples that appear on all number lists. Write out additional multiples for each number if there aren't any common multiples in the lists.
Find the least quantity that appears on both lists.
This is the LCM number.
Let’s take the LCM method example for the above method:
Example: Find the LCM of numbers 4 and 5 by listing methods.
Ans: LCM of 4 and 5 by the listing method:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ..
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, …
So Common Multiples are: 20, 40, …
according to the least method, the LCM of 4 and 5 is 20.
How to Find LCM by Prime Factorisation Method
Using the prime factorization method, we can find out the prime factors of the numbers.
Steps to be followed to calculate the LCM by the prime factors method is:
Step 1: Finding each number's prime factorization is the first step in computing the LCM using the prime factors approach.
Step 2: When you write each number as a product of primes.
Step 3: Now take the highest power of each prime number.
Step 4: To obtain the LCM, multiply the prime numbers.
Let’s take the LCM method example for the above method:
Example: Calculate the LCM of 50 and 100.
Ans: Steps to be followed to calculate LCM are:
Finding each number's prime factorization:
$50: 2 \times 5 \times 5$
$100: 2 \times 2 \times 5 \times 5$
When you write each number as a product of primes.
$50: 2 \times 5 \times 5$
$100: 2 \times 2 \times 5 \times 5$
Now take the highest power of each prime number. Here the highest power of 2 and 5 is 2. Therefore,
$2 \times 2 \times 5 \times 5$
To obtain the LCM, multiply the numbers
Multiplying $2 \times 2 \times 5 \times 5=100$
How to Find LCM by Division Method
LCM by Standard Division Method
To calculate the LCM of two numbers using the division method, we have to follow the steps given below:
Step 1: To find the LCM by division method, we write the given numbers in a row separately by commas, then divide the numbers by a common prime number. Find a prime number of a factor of at least one of the given numbers. Put this prime number to the left of the given numbers.
Step 2: We stop dividing after reaching the prime numbers. The product of common and uncommon prime factors is the LCM of given numbers. (It means if the prime number in step 1 is a factor of the number, divide the number by the prime and write the quotient below. If the prime number in step 1 is not a factor of the number, write the number in the row below as it is. Continue the steps until only one is left in the last row.)
Let’s take the LCM method example for the above method:
Examples: Find the least common multiple (LCM) of 6 and 12 using the division method.
Ans: Step-by-step explanation to solve LCM by the common division method is given below:
Step-by-Step Explanation to Solve LCM by Common Division Method
Solved Examples
Q1. Find the least common multiple (LCM) of 36 and 60 using the division method.
Ans: Step-by-step explanation to solve LCM by the common division method is given below:
LCM by Division Method
LCM of 36 and 60 is 2 ×2 × 3 × 3 × 5 = 180
Q2. What is the least common multiple of 980 and 9000 using the prime factorization method?
Ans: Steps to find LCM
Find the prime factorization of 980
980 = 2 × 2 × 5 × 7 × 7
Find the prime factorization of 9000
9000 = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5 × 7 × 7
LCM = 441000
Practice Questions:
Q1. Find the LCM of 4, 8, and 16 by using the listing method.
Ans: 16
Q2. Find the LCM of 14 and 16.
Ans: 112
Q3. Find the LCM using the prime factors method: 60 and 72.
Ans: 360
Q4. Find the least common multiple (LCM) using the division method of: 9, 12 and 36
Ans: 36
Summary
Learning about LCM can be helpful when trying to solve problems or puzzles. For example, if we have three numbers and want to find the smallest number that is a multiple of both of those numbers, we would use the LCM method. In this article, we learned about the Least Common Multiple (LCM) and how it can be used to simplify multiple problems. We also explored three methods for finding LCM, and explained how to solve it. Now that you have a better understanding of what LCM is and why it's important, continue learning more about this intriguing number in future articles!
FAQs on How To Take LCM of Numbers Easily
1. What is LCM in maths?
The LCM (Least Common Multiple) of two or more numbers is the smallest number that is exactly divisible by all the given numbers. In other words, it is the smallest common multiple they share. For example, multiples of 4 are 4, 8, 12, 16, … and multiples of 6 are 6, 12, 18, …; the smallest common multiple is 12, so LCM(4, 6) = 12.
2. How do you take LCM of two numbers?
To take the LCM of two numbers, list their multiples or use the prime factorization method to find the smallest common multiple. One common method is:
- Write the prime factorization of both numbers.
- Take each prime factor with the highest power.
- Multiply those factors.
3. What is the formula for LCM?
The formula to find LCM using HCF (GCD) is LCM × HCF = Product of the numbers. For two numbers a and b, LCM(a, b) = (a × b) / HCF(a, b). For example, for 12 and 18, HCF = 6, so LCM = (12 × 18) / 6 = 36.
4. How do you find LCM using prime factorization?
To find LCM using prime factorization, multiply the highest powers of all prime factors involved. Steps:
- Factor each number into primes.
- Select each prime with the greatest exponent.
- Multiply them together.
5. How do you find the LCM of three numbers?
To find the LCM of three numbers, use prime factorization and take the highest power of each prime factor from all numbers. Example:
- 6 = 2 × 3
- 8 = 2³
- 9 = 3²
6. What is the LCM of 12 and 15?
The LCM of 12 and 15 is 60. Prime factorization method:
- 12 = 2² × 3
- 15 = 3 × 5
7. What is the difference between LCM and HCF?
The LCM is the smallest common multiple of given numbers, while the HCF (Highest Common Factor) is the greatest common divisor of those numbers. For example, for 8 and 12:
- LCM = 24 (smallest number divisible by both)
- HCF = 4 (largest number dividing both)
8. Why do we use LCM in fractions?
We use LCM in fractions to find a common denominator when adding or subtracting unlike fractions. The LCM of denominators gives the smallest common denominator. Example: For 1/4 and 1/6, LCM of 4 and 6 is 12, so 1/4 = 3/12 and 1/6 = 2/12, making addition easier.
9. Can you give a simple example of how to calculate LCM?
A simple example of calculating LCM is finding LCM of 5 and 7 by listing multiples. Multiples of 5: 5, 10, 15, 20, 25, 30, 35… Multiples of 7: 7, 14, 21, 28, 35… The smallest common multiple is 35, so LCM(5, 7) = 35.
10. What are the common methods to find LCM?
The common methods to find LCM are listing multiples, prime factorization, and the division method. These include:
- Listing method: Write multiples until a common one appears.
- Prime factorization method: Multiply highest powers of primes.
- Division method: Divide numbers by common primes step by step.
