LCM of 36 and 40 is 360. LCM is a way of determining the smallest common multiple between any two numbers or more. High professional teachers recommend the article Least Common Multiple (LCM) as the best study source for students to master the LCM concept in-depth. Students can make use of this article while solving problems to enhance their logical and analytical thinking abilities. Let us have a look at how to find the least common multiple of 36 and 40 using prime factorisation, division method and a list of multiples in this article.
What is LCM of 36 and 40?
The answer to this question is 360.
How to Find LCM of 36 and 40?
The LCM of 36 and 40 can be obtained using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 36 and 40 Using Prime Factorisation Method
In the prime factorisation method, we calculate the LCM of given numbers by writing the prime factors of numbers individually. Hence the numbers 36 and 40 are expressed as;
36 = 2 × 2 × 3 × 3
40 = 2 × 2 × 2 × 5
LCM (36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 36 and 40 Using Division Method
In this method, to calculate the LCM, we divide the numbers 36 and 40 by their prime factors until we get the result as one in the complete row. The product of these divisors denotes the least common multiple of 36 and 40.
| 2 | 36 | 40 |
| 2 | 18 | 20 |
| 2 | 9 | 10 |
| 3 | 9 | 5 |
| 3 | 3 | 5 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (36, 40) = 2 × 2 × 2 × 3 × 3 × 5 = 360
LCM of 36 and 40 Using Listing the Multiples
Here, we list down the multiples of given numbers to find the least common multiple. Let us glance at the multiples of 36 and 40 given below.
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, ………..
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, ………
LCM (36, 40) = 360
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 36 and 40?
Solution: 360 is the smallest number that is divisible by both 36 and 40.
Q. 2: What is the LCM if the product of two numbers is 1440 and their GCD is 4?
Solution: Given
GCD = 4
Product of numbers = 1440
We know that
LCM × GCD = Product of numbers
LCM × 4 = 1440
LCM = 1440/4
LCM = 360
Hence the LCM is 360.
Frequently Asked Questions on LCM of 36 and 40
What is the LCM of 36 and 40?
Is the LCM of 36 and 40 the same as the HCF of 36 and 40?
4 is the highest common factor of 36 and 40. True or False.
Mention the methods used to find the LCM of 36 and 40.
The methods used to find the LCM of 36 and 40 are:
Prime Factorisation
Division Method
Listing the Multiples
What is the GCF if the LCM of 36 and 40 is 360?
GCF × LCM = 36 × 40
Given
LCM = 360
GCF × 360 = 36 × 40
GCF = 4
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