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.

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

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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.