LCM of 3, 4 and 9 is 36. LCM is abbreviated as Least Common multiple or Lowest common multiple. LCM is the easy method to find the smallest common multiples between two or more than two numbers.
The LCM of 3, 4 and 9 can be found by three methods which are used regularly.
What is the LCM of 3,4 and 9?
The Least Common Multiple or Lowest Common Multiple of 3, 4 and 9 is 36.
How to Find LCM of 3, 4 and 9?
Let us see the different methods for finding the LCM of 3, 4 and 9.
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 3, 4 and 9 Using Prime Factorisation Method
To find the Prime factorization of 3, 4 and 9, let’s look into the following steps:
1. Find the prime factorization of each number
3 = 31
4 = 22
9 = 32
2. LCM of 3, 4 and 9 is obtained by multiplying prime factors, which are raised to their respective highest power.
Hence, the LCM of 3, 4 and 9 by prime factorization is 22 × 32 = 36.
LCM of 3, 4 and 9 by Division Method
Here the given numbers are 3, 4 and 9.
Let us find the least common multiple of the given number.
First, let us divide the given number by the least prime number 2. suppose if it is not divisible by 2 we need to write down the same number as it is and continue the process till the remainder ends up with 1.
| 2 | 3 | 4 | 9 |
| 2 | 3 | 2 | 9 |
| 3 | 3 | 1 | 9 |
| 3 | 1 | 1 | 3 |
| 1 | 1 | 1 |
Hence, the least common multiple of the numbers 3, 4 and 9 is 36.
LCM= 2 × 2 × 3 × 3 = 36
LCM of 3, 4 and 9 by Listing Multiples
To calculate the LCM of 3, 4 and 9, let us list the multiples of 3,4 and 9.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, …
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …
Multiples of 9: 9, 18, 27, 36, 45…
Now let us see the steps to obtain the LCM of 3,4 and 9.
Step 1: List out a few multiples of 3,4 and 9.
Step 2: Now the common multiples from the multiples of 3,4 and 9 are 36, …
Step 3: The smallest common multiple of 3,4 and 9 is 36.
Hence the least common multiple of 3,4 and 9 = 36.
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Solved Examples
Example 1:
Find the smallest number that is divisible by 3,4 and 9 exactly?
Solution:
The smallest number that is divisible by 18 and 81 exactly is their LCM.
Therefore, the LCM of 3, 4 and 9 is 36.
Example 2:
Which of the following is the LCM of 3, 4 and 9?
a) 36 b)12 c)40 d)18
Solution:
The LCM of 3, 4 and 9 is 36.
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