LCM of 28, 36 and 45 is 1260. LCM of 28, 36 and 45 is the lowest number among all the common multiples of 28, 36 and 45. There are three regular methods to find out the LCM. LCM is defined as the smallest common multiple of two or more numbers.
What is the LCM of 28, 36 and 45?
The Least Common Multiple or Lowest Common Multiple of 28,36 and 45 is 1260.
How to Find LCM of 28, 36 and 45?
Regularly we use three different methods for finding the LCM of 28, 36 and 45.
- By Prime Factorisation
- By Division method
- By Listing the multiples
LCM of 28, 36 and 45 Using Prime Factorisation Method
Prime factorization is the process of finding the prime numbers which are multiplied together to get the original number.
Prime factorization of 28, 36 and 45 is:
28 = 2 × 2 × 7 = 22× 71
36= 2 × 2 × 3 × 3 = 22× 32
45 = 32× 51
LCM of 28, 36 and 45 can be obtained by multiplying prime factors raised to their highest powers.
Hence, the LCM of 28,36 and 45 by prime factorization is 1260.
LCM of 28, 36 and 45 by Division Method
To calculate the LCM of 28, 36 and 45 by division method, follow the below steps:
Step 1: Divide the numbers 28, 36 and 45 by the smallest prime number 2, such that the smallest prime number should divide the number completely.
Step 2: Now we will again divide the quotient of step 1 by the smallest prime number.
Step 3: Repeat the step until the quotient becomes 1.
The LCM of 28,36 and 45 by division method is 1260.
| 2 | 28 | 36 | 45 |
| 2 | 14 | 18 | 45 |
| 3 | 7 | 9 | 45 |
| 3 | 7 | 3 | 15 |
| 5 | 7 | 1 | 5 |
| 7 | 7 | 1 | 1 |
| 1 | 1 | 1 |
LCM = 2 × 2 × 3 × 3 × 5 × 7 =1260
LCM of 28, 36 and 45 by Listing Multiples
First to find the LCM of 28, 36 and 45 let us list the multiples of 28, 36 and 45.
Multiples of 28: 28, 56, 84, 112, 140, …
Multiples of 36: 36, 72, 108, 144, 180, …
Multiples of 45: 45, 90, 135, 180, 225, …
Step 1: List out a few multiples of 28, 36 and 45 as shown above.
Step 2: Now the common multiples from the multiples of 28, 36 and 45 are 1260, …
Step 3: The smallest common multiple of 28, 36 and 45 is 1260.
Hence the least common multiple of 28, 36 and 45 = 1260
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Solved Example
Example:
Find the smallest number that is divisible by 28, 36 and 45 exactly.
Solution:
The smallest number that is divisible by 28, 36 and 45 exactly is their LCM.
Therefore, the LCM of 28, 36 and 45 is 1260.
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