How to Find LCM of 2 Numbers?

To find the LCM of two numbers, identify their prime factors and calculate the product of the highest powers of these factors.

LCM stands for “Least Common Multiple.” It refers to the smallest positive integer divisible by two or more given integers without leaving a remainder. In other words, the LCM is the smallest number, a multiple of each given number.

LCM or the Least Common Multiple is calculated by various methods and the most common three methods are,

• Finding LCM using Listing Method
• Finding LCM using Prime Factorization Method
• Finding LCM using Division Method

Finding LCM using the listing method is achieved using the steps added below, suppose we have to find the LCM of two numbers P and Q then

Step 1: Find and list all the multiples of P and Q.

Step 2: Observe the multiples of P and Q and find the lowest common multiple among them.

Step 3: Now the smallest common multiple of these P and Q is the LCM of P and Q.

For Example, find the LCM of 6 and 8.

Solution:

List the multiple of 6 and 8

Multiples of 6 = 6, 12, 18, 24, 50, …

Multiples of 8 = 8, 16, 24, 32, 40, …

Least common multiple of 6 and 8 is, 24

Thus, the LCM of 6 and 8 is 24

In the prime factorization method, we write the prime factors of the numbers and then the factor with the highest exponent is the LCM of the number. Using the prime factorization method find the LCM of P and Q.

Step 1: Write the prime factors of P and Q.

Step 2: Write all the factors of P and Q in exponent form.

Step 3: Then we find the products of the factors with the highest exponents.

For Example, find the LCM of 16 and 18.

Solution:

Write prime factors of 16, and 18

16 = 2×2×2×2 = 24

18 = 2×3×3 = 2×32

LCM of 16 and 18 = 24×32

= 16×9 = 144

Thus, the LCM of 16 and 18 is 144.

Division method is the method that is used to find the LCM of the number quickly. We find the LCM of two numbers 12 and 15 by following the steps added below,

Step 1: Write the number in the format as shown in the image added below,

Step 2: Starting from the first prime number write a prime number that is a factor of any of the number. (Here 2 is factor of 12). Divide the numbers with the prime to reduce the numbers.

Step 3: Continue the same pattern and then start increasing to next prime number as required. (Here, 2 is also a factor of 6 so we again divide by 2)

Step 4: Continue the Step 2 with next prime till we reduce all the numbers to 1

Step 5: Here, both the numbers are reduce to 1 so the LCM is the product of all the prime factors so obtained.

Thus, LCM of 12 and 15 = 2×2×3×5 = 60

Let’s consider another example for the same.

Example: Find the LCM of 20 and 30.

Solution:

LCM of 20 and 30 is calculated as,

LCM of 20 and 30 = 2×2×3×5 = 60

Here, 60 is the smallest multiple of 20 and 30 that is completely divided by both 20 and 30.

Related Articles:

• Least Common Multiple (LCM): How to Find and Examples
• LCM Formula | Least Common Multiple Formula
• HCF and LCM: Definition, Formula, Full Form, Examples

In conclusion, mastering the method for finding the LCM of two numbers empowers individuals to solve mathematical problems efficiently and accurately. By understanding the principles of prime factorization and highest power selection, one can confidently determine the LCM and apply it in various mathematical contexts.

Define Lowest Common Multiple with an example.

We define LCM or the Lowest Common Multiple of two numbers as the number that is lowest in value and is the multiple of both numbers. For example, the Lowest Common Multiple(LCM) of 5 and 15 is 15.

How to Find the Least Common Multiple (LCM)?

Least Common Multiple (LCM) can easily be calculated using the given methods,

• Listing Method
• Prime Factorization Method
• Division Method

All these methods are discussed in the article.

What is the LCM of two Prime Numbers?

LCM of two prime numbers is the product of the numbers.

What is Relation Between HCF and LCM?

Relation between HCF and LCM is, for two numbers ‘a’ and ‘b’.

• “Product of a and b is equal to the product of HCF and LCM”
• LCM(a, b) × HCF(a, b) = a × b

What is the LCM of 25 and 75?

LCM of 25 and 75 is 75.

What is the LCM of 12 and 8?

LCM of 8 and 12 is 24.

What is the LCM of 24 and 36?

LCM of 24 and 36 is 72.

Can LCM of two numbers be smaller than both numbers?

No, the LCM of two numbers is always greater than or equal to the larger of the two numbers.

Can LCM of a set of numbers be zero?

No, the LCM of a set of numbers is always a positive integer.

Is LCM commutative?

Yes, the LCM is commutative, meaning that LCM(a, b) = LCM(b, a).

Can LCM of two numbers be equal to one of the numbers?

Yes, if one of the numbers is a factor of the other, then the LCM can be equal to the larger number.

What is Least Common Multiple Calculator?

Least Common Multiple (LCM) calculator is a tool or mathematical utility that calculates the least common multiple of two or more numbers. The LCM of two or more numbers is the smallest multiple that is evenly divisible by each of those numbers.