LCM of 144 and 169 is 24336. The LCM is the process to find the least common multiple between any two or more numbers. Experts formulated the article Prime Factorisation and Division Method for LCM and HCF to make the representation of least common multiple and highest common factors of given numbers an easy task. This article explains the concepts using the prime factorisation and division method with solved examples in a descriptive manner. Let us grasp the method of how to find the least common multiple of 144 and 169 in a detailed manner here.
What is LCM of 144 and 169?
The answer to this question is 24336.
How to Find LCM of 144 and 169?
The following methods are used to find the LCM of 144 and 169:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 144 and 169 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. Therefore 144 and 169 can be expressed as;
144 = 2 × 2 × 2 × 2 × 3 × 3
169 = 13 × 13
LCM (144, 169) = 2 × 2 × 2 × 2 × 3 × 3 × 13 × 13 = 24336
LCM of 144 and 169 Using Division Method
In this method, we divide the numbers 144 and 169 by a common prime number until the remainder is a prime number or one. The product of these divisors denotes the least common multiple of 144 and 169.
| 2 | 144 | 169 |
| 2 | 72 | 169 |
| 2 | 36 | 169 |
| 2 | 18 | 169 |
| 3 | 9 | 169 |
| 3 | 3 | 169 |
| 13 | 1 | 169 |
| 13 | 1 | 13 |
| x | 1 | 1 |
No more further division can be done.
Hence, LCM (144, 169) = 2 × 2 × 2 × 2 × 3 × 3 × 13 × 13 = 24336
LCM of 144 and 169 Using Listing the Multiples
In this method, we list down the multiples of 144 and 169 to determine the least common multiple among them. A few multiples of 144 and 169 are given below:
Multiples of 144: 144, 288, 432, 576, 720, 864, 1008, 1152, 1296, 1440,………….
Multiples of 169: 169, 338, 507, 676, 845, 1014, 1183, 1352, 1521, 1690, ………..
LCM (144, 169) = 24336
Related Articles
Video Lesson on Applications of LCM
Solved Examples
Q. 1: What is the smallest number that is divisible by both 144 and 169?
Solution: 24336 is the smallest number that is divisible by both 144 and 169.
Q. 2: The GCD and LCM of two numbers are 1 and 24336. If one number is 144, calculate the other number.
Solution: Let the other number be r.
We know that,
GCD × LCM = 144 × r
r = (GCD × LCM)/144
r = (1 × 24336)/144
r = 169
Hence the other number is 169.
Frequently Asked Questions on LCM of 144 and 169
What is the LCM of 144 and 169?
Is the LCM of 144 and 169 the same as the HCF of 144 and 169?
Is 23336 the LCM of 144 and 169?
What is the GCF if the LCM of 144 and 169 is 24336?
GCF × LCM = 144 × 169
Given
LCM = 24336
GCF × 24336 = 144 × 169
GCF = 1
Write the relation between GCF and LCM of 144 and 169.
The relation between GCF and LCM of 144 and 169 is
GCF × LCM = 144 × 169
GCF × LCM = 24336
Comments