Page 90 - ICSE Math 4

Mul ples of 24 are 24, 48, 72, 96, ...
So, L.C.M. of 8 and 24 is 24.

We can see that 8 is a factor of 24. So we can say that the greater number 24 is the
L.C.M. of 8 and 24.
L.C.M. of two or more numbers can be obtained by two methods. These methods are the

lis ng method and the common division method. Let’s know about them.
Listing Method

In this method, we list the mul ples of the given numbers and then look for the smallest
number that appears in each list to fi nd the L.C.M. of the given numbers.
Example 16: Find the L.C.M. of 4 and 8 by lis ng method.

Solu on: Step 1: List the mul ples of each number.
Mul ples of 4 = 4, 8 , 12, 16, 20, …

Mul ples of 8 = 8 , 16, 24, 32, 40, …
Step 2: Find the common mul ples of 4 and 8 that appear in the list.
8 and 16 are the two common mul ples of 4 and 8.

Step 3: Write the smallest or the least common mul ple of 4 and 8. Here 8
is the least common mul ple (L.C.M.) of 4 and 8.

So, L.C.M. of 4 and 8 is 8.

Common Division Method or Prime Factorization Method

Step 1: Arrange the numbers with commas in between.

Step 2: Divide at least one of the given numbers by the least (smallest) prime number
and bringing down the undivided numbers as it is.

Step 3: Repeat step 2 ll all the numbers are reduced to 1 in the last row.
Step 4: Mul ply all the prime numbers to get the L.C.M. of the given numbers.

Example 17: Find the L.C.M. of 11 and 16 by prime factoriza on method.

Solu on: Step 1: Write the given numbers 11 and 16 in a row by 11, 16
separa ng them using commas as shown.
Step 2: Choose the smallest prime number that divides at

least one of the given numbers. Here, only 16 is 2 11, 16
divisible by the smallest prime number, i.e., 2. 11, 8
So, bring down the number 11 that is not divisible

by 2 as it is.
Step 3: Keep dividing the numbers by choosing the smallest 2 11, 16
prime number. 2 11, 8
11, 4

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