Home / Maths / LCM of 10 and 40 - Calculation Methods and Solved Examples

LCM of 10 and 40 - Calculation Methods and Solved Examples

Last Updated on Jun 10, 2024

IMPORTANT LINKS

30 in words 50 in words 70 in words 40 in words Midpoint Formula Square Root 45000 in words Cube Root 1999 in roman numerals 13 in roman numerals 200 in roman numerals 70 in roman numerals Factors of 27 Factors of 16 Factors of 120 Square Root and Cube Root Squares and Square roots Types of Function Graphs Right Triangle Congruence Theorem 80 in Words

The Least Common Multiple (LCM) of 10 and 40 is 40. The LCM is the smallest positive integer that is divisible by both numbers without leaving a remainder. The multiples of 10 are (10, 20, 30, 40, 50, …) and the multiples of 40 are (40, 80, 120, 160, 200, …). You can learn to calculate the LCM of two numbers using various methods such as listing multiples, prime factorization, and division.

Check out the article on: Least Common Multiple

The LCM of 10 and 40
The LCM of 10 and 40 is 40. It is the smallest positive integer that is divisible by both 10 and 40 without leaving a remainder. Here, we will demonstrate various methods to calculate the LCM of 10 and 40.

Methods to Find the LCM of 10 and 40
The LCM of 10 and 40 can be found using the following methods:

Prime Factorisation

Division method

Listing the multiples

Using Prime Factorisation to Find the LCM of 10 and 40

Prime factorisation of 10 and 40 is:

10 = 2 x 5 = 2¹ x 5¹

40 = 2 x 2 x 2 x 5 = 2³ x 5¹

Therefore, LCM (10, 40) = 40

Using Division Method to Find the LCM of 10 and 40

In the division method, we divide the numbers (10, 40) by their common prime factors. The LCM of 10 and 40 is obtained by multiplying the divisors.

After division, LCM (10, 40) = 40

Using Listing the Multiples Method to Find the LCM of 10 and 40

In this method, we list the multiples of the given numbers and identify the common multiple.

The LCM (10, 40) = 40

Examples of LCM of 10 and 40
Let's say the product of two numbers is 500 and their Greatest Common Divisor (GCD) is 10. What is their LCM?
Given:
Product = 500
GCD = 10
Since LCM x GCD = Product of two numbers,
We can find the LCM as follows: LCM = Product of two numbers/ GCD
Therefore, LCM = 500/10 = 50
Hence, the LCM is 50.

Frequently Asked Questions

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, and Listing the multiples.

What is the LCM of 10 and 40?

The LCM of 10 and 40 is 40.

What is the GCF if the LCM of 10 and 40 is 40?

The GCF is 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 or LCM x GCF = 400.

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.

Report An Error