LCM of 10 and 40

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.

LCM of 10 and 40

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

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

Q1

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

Q2

What is the LCM of 10 and 40?

The LCM of 10 and 40 is 40.
Q3

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

Q4

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

Q5

In 28, 40, 45 and 5, find the LCM of 10 and 40.

The LCM of 10 and 40 is the smallest common multiple which is divisible evenly by the two given numbers. The number 40 satisfies this condition.

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