LCM of 21, 28, 36 and 45 is 1260. LCM of 21, 28, 36, and 45 is the smallest number among all common multiples of 21, 28, 36, and 45. The first few multiples of 21, 28, 36, and 45 are (21, 42, 63, 84, 105 . . .), (28, 56, 84, 112, 140 . . .), (36, 72, 108, 144, 180 . . .), and (45, 90, 135, 180, 225 . . .) respectively. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 21, 28, 36 and 45?
The answer to this question is 1260. The LCM of 21, 28, 36 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 21, 28, 36 and 45, is the smallest positive integer 1260 which is divisible by both 21, 28, 36 and 45 with no remainder.
How to Find LCM of 21, 28, 36 and 45?
LCM of 21, 28, 36 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 21, 28, 36 and 45 Using Prime Factorisation Method
The prime factorisation of 21, 28, 36 and 45, respectively, is given by:
21 = (3 × 7) = 31 × 71,
28 = (2 × 2 × 7) = 22 × 71,
36 = (2 × 2 × 3 × 3) = 22 × 32,
and
45 = (3 × 3 × 5) = 32 × 51
LCM (21, 28, 36, 45) = 1260
LCM of 21, 28, 36 and 45 Using Division Method
We’ll divide the numbers (21, 28, 36, 45) by their prime factors to get the LCM of 21, 28, 36 and 45 using the division method (preferably common). The LCM of 21, 28, 36 and 45 is calculated by multiplying these divisors.
| 2 | 21 | 28 | 36 | 45 |
| 2 | 12 | 14 | 18 | 45 |
| 2 | 6 | 7 | 9 | 45 |
| 2 | 3 | 7 | 9 | 45 |
| 3 | 1 | 7 | 3 | 15 |
| 5 | 1 | 7 | 1 | 5 |
| 7 | 1 | 7 | 1 | 1 |
| x | 1 | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (21, 28, 36, 45) = 1260
LCM of 21, 28, 36 and 45 Using Listing the Multiples
To calculate the LCM of 21, 28, 36 and 45 by listing out the common multiples, list the multiples as shown below
| Multiples of 21 | Multiples of 28 | Multiples of 36 | Multiples of 45 |
| 24 | 28 | 36 | 45 |
| 48 | 56 | 72 | 90 |
| 72 | 84 | 108 | 135 |
| 96 | 112 | 144 | 180 |
| ……… | …….. | ……… | …….. |
| 1260 | 1260 | 1260 | 1260 |
The smallest common multiple of 21, 28, 36 and 45 is 1260.
Therefore LCM (21, 28, 36, 45) = 1260
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LCM of 21, 28, 36 and 45 Solved Example
Question: Find the smallest number that is divisible by 21, 28, 36, 45 exactly.
Solution:
The value of LCM(21, 28, 36, 45) will be the smallest number that is exactly divisible by 21, 28, 36, and 45.
⇒ Multiples of 21, 28, 36, and 45:
Multiples of 21 = 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, . . . ., 1218, 1239, 1260, . . . .
Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, . . . ., 1148, 1176, 1204, 1232, 1260, . . . .
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 1152, 1188, 1224, 1260, . . . .
Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, . . . ., 1125, 1170, 1215, 1260, . . . .
Therefore, the LCM of 21, 28, 36, and 45 is 1260.
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