LCM of 108 and 144

LCM of 108 and 144 is the smallest number among all common multiples of 108 and 144. The first few multiples of 108 and 144 are (108, 216, 324, 432, 540, 648, 756, . . . ) and (144, 288, 432, 576, 720, 864, 1008, . . . ) respectively. There are 3 commonly used methods to find LCM of 108 and 144 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 108 and 144 is 432.

Explanation:

The LCM of two non-zero integers, x(108) and y(144), is the smallest positive integer m(432) that is divisible by both x(108) and y(144) without any remainder.

Let's look at the different methods for finding the LCM of 108 and 144.

• By Prime Factorization Method
• By Division Method
• By Listing Multiples

LCM of 108 and 144 by Prime Factorization

Prime factorization of 108 and 144 is (2 × 2 × 3 × 3 × 3) = 2² × 3³ and (2 × 2 × 2 × 2 × 3 × 3) = 2⁴ × 3² respectively. LCM of 108 and 144 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3³ = 432.
Hence, the LCM of 108 and 144 by prime factorization is 432.

LCM of 108 and 144 by Division Method

To calculate the LCM of 108 and 144 by the division method, we will divide the numbers(108, 144) by their prime factors (preferably common). The product of these divisors gives the LCM of 108 and 144.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 108 and 144. Write this prime number(2) on the left of the given numbers(108 and 144), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (108, 144) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
• Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 108 and 144 is the product of all prime numbers on the left, i.e. LCM(108, 144) by division method = 2 × 2 × 2 × 2 × 3 × 3 × 3 = 432.

LCM of 108 and 144 by Listing Multiples

To calculate the LCM of 108 and 144 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 108 (108, 216, 324, 432, 540, 648, 756, . . . ) and 144 (144, 288, 432, 576, 720, 864, 1008, . . . . )
• Step 2: The common multiples from the multiples of 108 and 144 are 432, 864, . . .
• Step 3: The smallest common multiple of 108 and 144 is 432.

∴ The least common multiple of 108 and 144 = 432.

☛ Also Check:

• LCM of 36 and 42 - 252
• LCM of 36 and 40 - 360
• LCM of 35 and 70 - 70
• LCM of 35 and 60 - 420
• LCM of 35 and 55 - 385
• LCM of 35 and 49 - 245
• LCM of 35 and 45 - 315

FAQs on LCM of 108 and 144

What is the LCM of 108 and 144?

The LCM of 108 and 144 is 432. To find the least common multiple of 108 and 144, we need to find the multiples of 108 and 144 (multiples of 108 = 108, 216, 324, 432; multiples of 144 = 144, 288, 432, 576) and choose the smallest multiple that is exactly divisible by 108 and 144, i.e., 432.

What is the Relation Between GCF and LCM of 108, 144?

The following equation can be used to express the relation between GCF and LCM of 108 and 144, i.e. GCF × LCM = 108 × 144.

If the LCM of 144 and 108 is 432, Find its GCF.

LCM(144, 108) × GCF(144, 108) = 144 × 108
Since the LCM of 144 and 108 = 432
⇒ 432 × GCF(144, 108) = 15552
Therefore, the greatest common factor (GCF) = 15552/432 = 36.

Which of the following is the LCM of 108 and 144? 50, 16, 432, 35

The value of LCM of 108, 144 is the smallest common multiple of 108 and 144. The number satisfying the given condition is 432.

How to Find the LCM of 108 and 144 by Prime Factorization?

To find the LCM of 108 and 144 using prime factorization, we will find the prime factors, (108 = 2 × 2 × 3 × 3 × 3) and (144 = 2 × 2 × 2 × 2 × 3 × 3). LCM of 108 and 144 is the product of prime factors raised to their respective highest exponent among the numbers 108 and 144.
⇒ LCM of 108, 144 = 2⁴ × 3³ = 432.