LCM of 14 and 36 is 252. LCM denotes the smallest positive number which is a multiple of two or more numbers. Students who aspire to learn the LCM concept thoroughly are advised to follow the article designed by experts who hold years of experience. LCM with Examples is the best study guide to enhance the knowledge of the LCM concept and improve the skills required to score better marks in exams. Here, we will learn how to find the least common multiple of 14 and 36 in detail.
What is LCM of 14 and 36?
The answer to this question is 252.
How to Find LCM of 14 and 36?
LCM of 14 and 36 can be determined by using three methods:
- Prime Factorisation
- Division method
- Listing the Multiples
LCM of 14 and 36 Using Prime Factorisation Method
In the prime factorisation method, the given natural numbers are expressed as the product of prime factors. Hence, the numbers 14 and 36 can be expressed as;
14 = 2 × 7
36 = 2 × 2 × 3 × 3
LCM (14, 36) = 2 × 2 × 3 × 3 × 7 = 252
LCM of 14 and 36 Using Division Method
In this method, we divide the numbers 14 and 36 by a common prime number until the remainder is a prime number or one. The product of these divisors depicts the least common multiple of 14 and 36.
| 2 | 14 | 36 |
| 2 | 7 | 18 |
| 3 | 7 | 9 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (14, 36) = 2 × 2 × 3 × 3 × 7 = 252
LCM of 14 and 36 Using Listing the Multiples
In this method, we list down the multiples of given natural numbers to find the lowest common multiple among them. The multiples of 14 and 36 are as follows:
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ……., 224, 238, 252, ……….
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, ….
LCM (14, 36) = 252
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 14 and 36?
Solution: 252 is the smallest number that is divisible by both 14 and 36.
2. The product of the two numbers is 504. Find the LCM if their GCD is 2.
Solution: Given
GCD = 2
Product of numbers = 504
We know that
GCD × LCM = Product of numbers
LCM = Product of numbers / GCD
LCM = 504 / 2
LCM = 252
Hence the LCM is 252.
Frequently Asked Questions on LCM of 14 and 36
What is the LCM of 14 and 36?
Is the LCM of 14 and 36 the same as the HCF of 14 and 36?
How to find the LCM of 14 and 36 by prime factorisation?
In the prime factorisation method, the given numbers are expressed as the product of prime factors
14 = 2 × 7
36 = 2 × 2 × 3 × 3
LCM (14, 36) = 2 × 2 × 3 × 3 × 7 = 252
Hence, 252 is the LCM of 14 and 36 by prime factorisation
Name the methods used to determine the LCM of 14 and 36.
The following methods are used to determine the LCM of 14 and 36
Prime Factorisation
Division Method
Listing the Multiples
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