LCM of 35 and 40 is 280. LCM denotes the smallest positive number that is a multiple of two or more numbers. It is essential to choose the right study tool for a thorough understanding of the LCM concept. To overcome this issue, subject experts prepared the article Least Common Multiple (LCM) in a simple language as per the students’ understanding capacity. Let us glance at the method of finding the least common multiple of 35 and 40 with the help of the examples and FAQs in this article.
What is LCM of 35 and 40?
The answer to this question is 280.
How to Find LCM of 35 and 40?
The LCM of 35 and 40 can be obtained by using the following methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 35 and 40 Using Prime Factorisation Method
In this method, the given natural numbers are expressed as the product of prime factors. Hence the numbers 35 and 40 can be expressed as;
35 = 5 × 7
40 = 2 × 2 × 2 × 5
LCM (35, 40) = 2 × 2 × 2 × 5 × 7 = 280
LCM of 35 and 40 Using Division Method
In this method, we divide the numbers 35 and 40 by a common prime number until the remainder is a prime number or one. The product of these divisors represents the least common multiple of 35 and 40.
| 2 | 35 | 40 |
| 2 | 35 | 20 |
| 2 | 35 | 10 |
| 5 | 35 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (35, 40) = 2 × 2 × 2 × 5 × 7 = 280
LCM of 35 and 40 Using Listing the Multiples
Here, we list down the multiples of given natural numbers to find the lowest common multiple among them. Let us glance at the multiples of 35 and 40 from the table given below.
| Multiples of 35 | Multiples of 40 |
| 35 | 40 |
| 70 | 80 |
| 105 | 120 |
| 140 | 160 |
| 175 | 200 |
| 210 | 240 |
| 245 | 280 |
| 280 | 320 |
LCM (35, 40) = 280
Related Articles
Prime Factorization and Division Method for LCM and HCF
Video Lesson on Applications of LCM
Solved Examples
1. What is the smallest number that is divisible by both 35 and 40?
Solution: 280 is the smallest number that is divisible by both 35 and 40.
2. The GCD and LCM of two numbers are 5 and 280. If one number is 35, what is the other number?
Solution: Let the other number be m
We know that,
GCD × LCM = 35 × m
m = (GCD × LCM)/ 35
m = (5 × 280) / 35
m = 40
Hence the other number is 40.
Frequently Asked Questions on LCM of 35 and 40
What is the LCM of 35 and 40?
Is the LCM of 35 and 40 the same as the HCF of 35 and 40?
7 is the highest common factor of 35 and 40. True or False.
Determine the GCF if the LCM of 35 and 40 is 280.
GCF × LCM = 35 × 40
Given
LCM = 280
GCF × 280 = 35 × 40
GCF = 5
What are the methods used to find the LCM of 35 and 40?
The methods used to find the LCM of 35 and 40 are
Prime Factorisation
Division Method
Listing the Multiples
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