LCM of 40 and 60 is 120. In the multiples of the numbers 40 and 60, the value which can be divisible evenly is the LCM. Least common multiple of 40 and 60 is the common multiple of two numbers which is obtained using the multiplication operation. (40, 80, 120, 160, 200, 240, ….) and (60, 120, 180, 240, 300, 360, ….) are the multiples of 40 and 60. The LCM of two numbers is found using the listing of multiples method, prime factorization method and by division method.
Also read: Least common multiple
What is LCM of 40 and 60?
The answer to this question is 120. The LCM of 40 and 60 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40 and 60, is the smallest positive integer 120 which is divisible by both 40 and 60 with no remainder.
How to Find LCM of 40 and 60?
LCM of 40 and 60 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40 and 60 Using Prime Factorisation Method
The prime factorisation of 40 and 60, respectively, is given by:
40 = 2 x 2 x 2 x 5 = 2³ x 5¹
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
LCM (40, 60) = 120
LCM of 40 and 60 Using Division Method
We’ll divide the numbers (40, 60) by their prime factors to get the LCM of 40 and 60 using the division method (preferably common). The LCM of 40 and 60 is calculated by multiplying these divisors.
| 2 | 40 | 60 |
| 2 | 20 | 30 |
| 2 | 10 | 15 |
| 3 | 5 | 15 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (40, 60) = 120
LCM of 40 and 60 Using Listing the Multiples
To calculate the LCM of 40 and 60 by listing out the common multiples, list the multiples as shown below:
| Multiples of 40 | Multiples of 60 |
| 40 | 60 |
| 80 | 120 |
| 120 | 180 |
| 160 | 240 |
| 200 | 300 |
LCM (40, 60) = 120
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Video Lesson on Applications of LCM
LCM of 40 and 60 Solved Examples
Question. Find the smallest number exactly divisible by 40 and 60.
Solution:
We know that
LCM is the smallest number exactly divisible by 40 and 60.
Multiples of 40 = 40, 80, 120, 160, 200, ….
Multiples of 60 = 60, 120, 180, 240, 300, …..
Hence, the LCM of 40 and 60 is 120.
Frequently Asked Questions on LCM of 40 and 60
List the methods used to find the LCM of 40 and 60.
The methods used to find the LCM of 40 and 60 are:
Prime Factorisation
Division method
Listing the multiples
With the help of the prime factorisation method, determine the LCM of 40 and 60.
We should know the factors first to determine the LCM
40 = 2 x 2 x 2 x 5 = 2³ x 5¹
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
LCM is the product of prime factors raised to the highest exponent among 40 and 60.
LCM of 40 and 60 = 120
What is the GCF if the LCM of 40 and 60 is 120?
LCM x GCF = 40 x 60
As the LCM = 120
120 x GCF = 2400
GCF = 2400/120 = 20
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