LCM of 40, 42 and 45 is 2520. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. LCM of 40, 42, and 45 is the smallest number among all common multiples of 40, 42, and 45. The first few multiples of 40, 42, and 45 are (40, 80, 120, 160, 200 . . .), (42, 84, 126, 168, 210 . . .), and (45, 90, 135, 180, 225 . . .) respectively. 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 40, 42 and 45?
The answer to this question is 2520. The LCM of 40, 42 and 45 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40, 42 and 45, is the smallest positive integer 2520 which is divisible by both 40, 42 and 45 with no remainder.
How to Find LCM of 40, 42 and 45?
LCM of 40, 42 and 45 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40, 42 and 45 Using Prime Factorisation Method
The prime factorisation of 40, 42 and 45, respectively, is given by:
40 = (2 × 2 × 2 × 5) = 23 × 51,
42 = (2 × 3 × 7) = 21 × 31 × 71, and
45 = (3 × 3 × 5) = 32 × 51
LCM (40, 42, 45) = 2520
LCM of 40, 42 and 45 Using Division Method
We’ll divide the numbers (40, 42, 45) by their prime factors to get the LCM of 40, 42 and 45 using the division method (preferably common). The LCM of 40, 42 and 45 is calculated by multiplying these divisors.
| 2 | 40 | 42 | 45 |
| 2 | 20 | 21 | 45 |
| 2 | 10 | 21 | 45 |
| 5 | 5 | 21 | 45 |
| 3 | 1 | 21 | 9 |
| 3 | 1 | 7 | 3 |
| 7 | 1 | 7 | 1 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (40, 42, 45) = 2520
LCM of 40, 42 and 45 Using Listing the Multiples
To calculate the LCM of 40, 42 and 45 by listing out the common multiples, list the multiples as shown below
| Multiples of 40 | Multiples of 42 | Multiples of 45 |
| 40 | 42 | 45 |
| 80 | 84 | 90 |
| 120 | 126 | 135 |
| ……. | …… | …… |
| 2520 | 2520 | 2520 |
The smallest common multiple of 40, 42 and 45 is 72.
Therefore LCM (40, 42, 45) = 2520
Related Articles
Video Lesson on Applications of LCM
LCM of 40, 42 and 45 Solved Example
Question: Find the smallest number that is divisible by 40, 42, 45 exactly.
Solution:
The value of LCM(40, 42, 45) will be the smallest number that is exactly divisible by 40, 42, and 45.
⇒ Multiples of 40, 42, and 45:
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 2440, 2480, 2520, . . . .
Multiples of 42 = 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, . . . ., 2436, 2478, 2520, . . . .
Multiples of 45 = 45, 90, 135, 180, 225, 270, 315, 360, 405, 450, . . . ., 2430, 2475, 2520, . . . .
Therefore, the LCM of 40, 42, and 45 is 2520.
Comments