LCM of 72 and 108

LCM of 72 and 108 is the smallest number among all common multiples of 72 and 108. The first few multiples of 72 and 108 are (72, 144, 216, 288, . . . ) and (108, 216, 324, 432, 540, . . . ) respectively. There are 3 commonly used methods to find LCM of 72 and 108 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 72 and 108 is 216.

Explanation:

The LCM of two non-zero integers, x(72) and y(108), is the smallest positive integer m(216) that is divisible by both x(72) and y(108) without any remainder.

The methods to find the LCM of 72 and 108 are explained below.

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

LCM of 72 and 108 by Listing Multiples

To calculate the LCM of 72 and 108 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 72 (72, 144, 216, 288, . . . ) and 108 (108, 216, 324, 432, 540, . . . . )
• Step 2: The common multiples from the multiples of 72 and 108 are 216, 432, . . .
• Step 3: The smallest common multiple of 72 and 108 is 216.

∴ The least common multiple of 72 and 108 = 216.

LCM of 72 and 108 by Division Method

To calculate the LCM of 72 and 108 by the division method, we will divide the numbers(72, 108) by their prime factors (preferably common). The product of these divisors gives the LCM of 72 and 108.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 72 and 108. Write this prime number(2) on the left of the given numbers(72 and 108), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (72, 108) 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 72 and 108 is the product of all prime numbers on the left, i.e. LCM(72, 108) by division method = 2 × 2 × 2 × 3 × 3 × 3 = 216.

LCM of 72 and 108 by Prime Factorization

Prime factorization of 72 and 108 is (2 × 2 × 2 × 3 × 3) = 2³ × 3² and (2 × 2 × 3 × 3 × 3) = 2² × 3³ respectively. LCM of 72 and 108 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3³ = 216.
Hence, the LCM of 72 and 108 by prime factorization is 216.

☛ Also Check:

• LCM of 75 and 80 - 1200
• LCM of 12 and 32 - 96
• LCM of 150 and 180 - 900
• LCM of 5 and 12 - 60
• LCM of 4 and 24 - 24
• LCM of 70, 105 and 175 - 1050
• LCM of 56 and 98 - 392

FAQs on LCM of 72 and 108

What is the LCM of 72 and 108?

The LCM of 72 and 108 is 216. To find the LCM of 72 and 108, we need to find the multiples of 72 and 108 (multiples of 72 = 72, 144, 216, 288; multiples of 108 = 108, 216, 324, 432) and choose the smallest multiple that is exactly divisible by 72 and 108, i.e., 216.

Which of the following is the LCM of 72 and 108? 35, 12, 45, 216

The value of LCM of 72, 108 is the smallest common multiple of 72 and 108. The number satisfying the given condition is 216.

What is the Least Perfect Square Divisible by 72 and 108?

The least number divisible by 72 and 108 = LCM(72, 108)
LCM of 72 and 108 = 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 72 and 108 = LCM(72, 108) × 2 × 3 = 1296 [Square root of 1296 = √1296 = ±36]
Therefore, 1296 is the required number.

If the LCM of 108 and 72 is 216, Find its GCF.

LCM(108, 72) × GCF(108, 72) = 108 × 72
Since the LCM of 108 and 72 = 216
⇒ 216 × GCF(108, 72) = 7776
Therefore, the GCF = 7776/216 = 36.

What are the Methods to Find LCM of 72 and 108?

The commonly used methods to find the LCM of 72 and 108 are:

• Listing Multiples
• Division Method
• Prime Factorization Method