LCM of 45 and 86 is 3870. The least or smallest common multiple of any two or more given natural numbers are defined as LCM. Students who wish to learn the method of finding LCM and HCF using the prime factorisation and division method effectively are suggested to refer to the article Prime Factorisation and Division Method for LCM and HCF on a regular basis. This article has been designed by experts to provide the best study resource for students. Let us study how to calculate the least common multiple of 45 and 86 with simple steps in this article.
What is LCM of 45 and 86?
The answer to this question is 3870.
How to Find LCM of 45 and 86?
The following methods are used to find the LCM of 45 and 86:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 45 and 86 Using Prime Factorisation Method
In this method, the given natural numbers are written as the product of prime factors. The least common multiple will be the product of all prime factors with the highest degree.
45 = 3 × 3 × 5
86 = 2 × 43
LCM (45, 86) = 2 × 3 × 3 × 5 × 43 = 3870
LCM of 45 and 86 Using Division Method
In this method, we divide the numbers 45 and 86 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 45 and 86.
| 2 | 45 | 86 |
| 3 | 45 | 43 |
| 3 | 15 | 43 |
| 5 | 5 | 43 |
| 43 | 1 | 43 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (45, 86) = 2 × 3 × 3 × 5 × 43 = 3870
LCM of 45 and 86 Using Listing the Multiples
In this method, we list out the multiples of 45 and 86 to find their least common multiple. The multiples of 45 and 86 are given below.
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450,……….
Multiples of 86: 86, 172, 258, 344, 430, 516, 602, 688, 774, 860,………
LCM (45, 86) = 3870
Related Articles
Video Lesson on Applications of LCM
Solved Examples
Q. 1: The GCD and LCM of two numbers are 1 and 3870. If one number is 86, calculate the other number.
Solution: Let the other number be n
We know that,
GCD × LCM = 86 × n
n = (GCD × LCM)/86
n = (1 × 3870)/86
n = 45
Hence the other number is 45.
Q. 2: What is the smallest number that is divisible by both 45 and 86?
Solution: 3870 is the smallest number that is divisible by both 45 and 86.
Frequently Asked Questions on LCM of 45 and 86
What is the LCM of 45 and 86?
Is the LCM of 45 and 86 the same as the HCF of 45 and 86?
3870 is the LCM of 45 and 86. True or False.
Find the LCM of 45 and 86 using Prime Factorisation.
Here, we express the given numbers as the product of prime factors
45 = 3 × 3 × 5
86 = 2 × 43
LCM (45, 86) = 2 × 3 × 3 × 5 × 43 = 3870
Write the relation between GCF and LCM of 45 and 86.
The relation between GCF and LCM of 45 and 86 is
GCF × LCM = 45 × 86
GCF × LCM = 3870
Comments