LCM of 28, 36, 45, and 60 is 1260. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor is the positive integer that is a common multiple to the given set of numbers. Here the given set of numbers are 28, 36, 45 and 60. The smallest common multiple for all these numbers among many is 1260, and hence it is the LCM. You can refer to HCF and LCM to understand the difference between HCF and LCM.
What is LCM of 28, 36, 45, and 60
The Least Common Multiple or Lowest Common Multiple of 28, 36, 45, and 60 is 1260.
How to Find LCM of 28, 36, 45, and 60?
LCM of 28, 36, 45, and 60 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 28, 36, 45, and 60 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 28, 36, 45, and 60can be expressed as;
28 = 2 x 2 x 7
36 = 2 x 2 x 3 x 3
45 = 3 x 3 x 5
60 = 2 x 2 x 3 x 5
LCM (28, 36, 45, 60) = 2 x 2 x 3 x 3 x 5 x 7 = 1260
LCM of 28, 36, 45, and 60 Using Division Method
In the Division Method, the given set of numbers are written in the same row separated by a comma. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
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2 |
28 |
36 |
45 |
60 |
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2 |
14 |
18 |
45 |
30 |
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3 |
7 |
9 |
45 |
15 |
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5 |
7 |
3 |
15 |
5 |
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3 |
7 |
3 |
3 |
1 |
|
7 |
7 |
1 |
1 |
1 |
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x |
1 |
1 |
1 |
1 |
LCM (28, 36, 45, 60) = 2 x 2 x 3 x 3 x 5 x 7 = 1260
LCM of 28, 36, 45, and 60 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 28, 36, 45, and 60
Multiples of 28: 28, 56, 84, 112…1092, 1120, 1148…, 420, 427… 1260, 1288, 1316…
Multiples of 36: 36, 72, 108, 144,….684, 720, 756,.., 1152, 1188,.. 441, 1260, 1296, 1332 …
Multiples of 45: 45, 90, 135, …., 945, 990, 1035…,441, 1215, 1260, 1305..
Multiples of 60: 60, 120, 180…720, 780, 840,…440, 1200, 1260, 1320…
LCM (28, 36, 45, 60) = 1260
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 28, 36, 45, and 60?
Answer: 1260 is the smallest number that is divisible by 28, 36, 45, and 60.
What is the LCM of 28 and 36?
Answer: LCM of 28 and 36 is 252.
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