LCM of 40, 36 and 126 is 2520. 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. The smallest number among all common multiples of 40, 36, and 126 is the LCM of 40, 36, and 126. (40, 80, 120, 160, 200…), (36, 72, 108, 144, 180…), and (126, 252, 378, 504, 630…), respectively, are the first few multiples of 40, 36, and 126.
Also read: Least common multiple
What is LCM of 40, 36 and 126?
The answer to this question is 2520. The LCM of 40, 36 and 126 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40, 36 and 126, is the smallest positive integer 2520 which is divisible by both 40, 36 and 126 with no remainder.
How to Find LCM of 40, 36 and 126?
LCM of 40, 36 and 126 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40, 36 and 126 Using Prime Factorisation Method
The prime factorisation of 40, 36 and 126, respectively, is given by:
40 = (2 × 2 × 2 × 5) = 23 × 51,
36 = (2 × 2 × 3 × 3) = 22 × 32, and
126 = (2 × 3 × 3 × 7) = 21 × 32 × 71
LCM (40, 36, 126) = 2520
LCM of 40, 36 and 126 Using Division Method
We’ll divide the numbers (40, 36, 126) by their prime factors to get the LCM of 40, 36 and 126 using the division method (preferably common). The LCM of 40, 36 and 126 is calculated by multiplying these divisors.
| 2 | 40 | 36 | 126 |
| 2 | 20 | 18 | 63 |
| 2 | 10 | 9 | 63 |
| 3 | 5 | 9 | 63 |
| 3 | 5 | 3 | 21 |
| 5 | 5 | 1 | 7 |
| 7 | 1 | 1 | 7 |
| x | 1 | 1 | 1 |
No further division can be done.
Hence, LCM (40, 36, 126) = 2520
LCM of 40, 36 and 126 Using Listing the Multiples
To calculate the LCM of 40, 36 and 126 by listing out the common multiples, list the multiples as shown below
| Multiples of 40 | Multiples of 36 | Multiples of 126 |
| 40 | 36 | 126 |
| 80 | 72 | 252 |
| 120 | 108 | 378 |
| 160 | 144 | 504 |
| ……. | ……. | ……. |
| 2520 | 2520 | 2520 |
The smallest common multiple of 40, 36 and 126 is 2520.
Therefore LCM (40, 36, 126) = 2520
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LCM of 40, 36 and 126 Solved Example
Question: Find the smallest number that is divisible by 40, 36, 126 exactly.
Solution:
The value of LCM(40, 36, 126) will be the smallest number that is exactly divisible by 40, 36, and 126.
⇒ Multiples of 40, 36, and 126:
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, . . . ., 2440, 2480, 2520, . . . .
Multiples of 36 = 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, . . . ., 2448, 2484, 2520, . . . .
Multiples of 126 = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, . . . ., 2142, 2268, 2394, 2520, . . . .
Therefore, the LCM of 40, 36, and 126 is 2520.
Frequently Asked Questions on LCM of 40, 36 and 126
What is the LCM of 40, 36 and 126?
List the methods used to find the LCM of 40, 36 and 126.
Which of the following is the LCM of 40, 36, and 126? 2520, 18, 105, 30
What is the Least Perfect Square Divisible by 40, 36, and 126?
LCM of 40, 36, and 126 = 2 × 2 × 2 × 3 × 3 × 5 × 7 [Incomplete pair(s): 2, 5, 7] ⇒ Least perfect square divisible by each 40, 36, and 126 = LCM(40, 36, 126) × 2 × 5 × 7 = 176400 [Square root of 176400 = √176400 = ±420] Therefore, 176400 is the required number.
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