LCM of 10 and 40 is 40. Among the multiples of 10 and 40, the number evenly divisible by 10 and 40 shows the LCM. Least common multiple of 10 and 40 is the common multiple we get using the multiplication operation. (10, 20, 30, 40, 50, ….) and (40, 80, 120, 160, 200, ….) are the multiples of 10 and 40. Students can learn to calculate the LCM of two numbers by listing multiples, prime factorization and division methods.
Also read: Least common multiple
What is LCM of 10 and 40?
The answer to this question is 40. The LCM of 10 and 40 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 40, is the smallest positive integer 40 which is divisible by both 10 and 40 with no remainder.
How to Find LCM of 10 and 40?
LCM of 10 and 40 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 40 Using Prime Factorisation Method
The prime factorisation of 10 and 40, respectively, is given by:
10 = 2 x 5 = 2¹ x 5¹
40 = 2 x 2 x 2 x 5 = 2³ x 5¹
LCM (10, 40) = 40
LCM of 10 and 40 Using Division Method
We’ll divide the numbers (10, 40) by their prime factors to get the LCM of 10 and 40 using the division method (preferably common). The LCM of 10 and 40 is calculated by multiplying these divisors.
|
2 |
10 |
40 |
|
2 |
5 |
20 |
|
2 |
5 |
10 |
|
5 |
5 |
5 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (10, 40) = 40
LCM of 10 and 40 Using Listing the Multiples
To calculate the LCM of 10 and 40 by listing out the common multiples, list the multiples as shown below
|
Multiples of 10 |
Multiples of 40 |
|
10 |
40 |
|
20 |
80 |
|
30 |
120 |
|
40 |
160 |
|
50 |
200 |
LCM (10, 40) = 40
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 10 and 40 Solved Examples
Question: Product of two numbers is 400. What is the LCM if GCD is 10?
Solution:
It is given that
Product = 400
GCD = 10
We know that
LCM x GCD = Product of two numbers
LCM = Product of two numbers/ GCD
LCM = 400/10 = 40
Hence, the LCM is 40.
Frequently Asked Questions on LCM of 10 and 40
Show the methods we can use to determine the LCM of 10 and 40.
The methods we can use to determine the LCM of 10 and 40 are
Prime Factorisation
Division method
Listing the multiples
What is the LCM of 10 and 40?
What is the GCF if the LCM of 10 and 40 is 40?
LCM x GCF = 10 x 40
As the LCM = 40
40 x GCF = 400
GCF = 400/40 = 10
Write the relation between LCM and GCF of 10 and 40.
The relation between LCM and GCF of 10 and 40 is
LCM x GCF = 10 x 40
LCM x GCF = 400
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