krit.club logo

LCM - Basics

Grade 4CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

To find the LCM of two numbers using the Listing Method:

  1. List the first few multiples of the first number.
  2. List the first few multiples of the second number.
  3. Identify the common multiples from both lists.
  4. Select the smallest number among the common multiples.

📐Formulae

LCM=Smallest Common Multiple\text{LCM} = \text{Smallest Common Multiple}

Multiples of 2={2,4,6,8,10,… }\text{Multiples of } 2 = \{2, 4, 6, 8, 10, \dots\}

💡Examples

Problem 1:

Find the LCM of 44 and 66.

Solution:

Step 1: List the multiples of 44. Multiples of 4=4,8,12,16,20,24,28,32,36,…4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, \dots

Step 2: List the multiples of 66. Multiples of 6=6,12,18,24,30,36,…6 = 6, 12, 18, 24, 30, 36, \dots

Step 3: Find the common multiples. Common multiples of 44 and 66 are 12,24,36,…12, 24, 36, \dots

Step 4: Identify the smallest common multiple. The smallest number is 1212.

Therefore, the LCM of 44 and 66 is 1212.

Explanation:

We list the multiples of both numbers and look for the first number that appears in both lists. 1212 is the first number that is a multiple of both 44 and 66.

Problem 2:

Find the LCM of 3,5,3, 5, and 1010.

Solution:

Multiples of 3=3,6,9,12,15,18,21,24,27,30,33,…3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots Multiples of 5=5,10,15,20,25,30,35,…5 = 5, 10, 15, 20, 25, 30, 35, \dots Multiples of 10=10,20,30,40,…10 = 10, 20, 30, 40, \dots

Common multiple for all three numbers is 30,60,…30, 60, \dots Smallest common multiple = 3030.

So, LCM(3,5,10)=30\text{LCM}(3, 5, 10) = 30.

Explanation:

When finding the LCM of three numbers, we find the multiples of all three and identify the smallest number that is present in all three lists.