LCM of 54 and 72

LCM of 54 and 72 is the smallest number among all common multiples of 54 and 72. The first few multiples of 54 and 72 are (54, 108, 162, 216, 270, 324, . . . ) and (72, 144, 216, 288, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 54 and 72 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 54 and 72 is 216.

Explanation:

The LCM of two non-zero integers, x(54) and y(72), is the smallest positive integer m(216) that is divisible by both x(54) and y(72) without any remainder.

Let's look at the different methods for finding the LCM of 54 and 72.

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

LCM of 54 and 72 by Prime Factorization

Prime factorization of 54 and 72 is (2 × 3 × 3 × 3) = 2¹ × 3³ and (2 × 2 × 2 × 3 × 3) = 2³ × 3² respectively. LCM of 54 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3³ = 216.
Hence, the LCM of 54 and 72 by prime factorization is 216.

LCM of 54 and 72 by Listing Multiples

To calculate the LCM of 54 and 72 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 54 (54, 108, 162, 216, 270, 324, . . . ) and 72 (72, 144, 216, 288, 360, . . . . )
• Step 2: The common multiples from the multiples of 54 and 72 are 216, 432, . . .
• Step 3: The smallest common multiple of 54 and 72 is 216.

∴ The least common multiple of 54 and 72 = 216.

LCM of 54 and 72 by Division Method

To calculate the LCM of 54 and 72 by the division method, we will divide the numbers(54, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 54 and 72.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 54 and 72. Write this prime number(2) on the left of the given numbers(54 and 72), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (54, 72) 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 54 and 72 is the product of all prime numbers on the left, i.e. LCM(54, 72) by division method = 2 × 2 × 2 × 3 × 3 × 3 = 216.

☛ Also Check:

• LCM of 12 and 45 - 180
• LCM of 48, 56 and 72 - 1008
• LCM of 18, 24 and 30 - 360
• LCM of 6 and 9 - 18
• LCM of 72 and 24 - 72
• LCM of 12 and 40 - 120
• LCM of 24 and 40 - 120

FAQs on LCM of 54 and 72

What is the LCM of 54 and 72?

The LCM of 54 and 72 is 216. To find the LCM (least common multiple) of 54 and 72, we need to find the multiples of 54 and 72 (multiples of 54 = 54, 108, 162, 216; multiples of 72 = 72, 144, 216, 288) and choose the smallest multiple that is exactly divisible by 54 and 72, i.e., 216.

What are the Methods to Find LCM of 54 and 72?

The commonly used methods to find the LCM of 54 and 72 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

If the LCM of 72 and 54 is 216, Find its GCF.

LCM(72, 54) × GCF(72, 54) = 72 × 54
Since the LCM of 72 and 54 = 216
⇒ 216 × GCF(72, 54) = 3888
Therefore, the greatest common factor (GCF) = 3888/216 = 18.

What is the Least Perfect Square Divisible by 54 and 72?

The least number divisible by 54 and 72 = LCM(54, 72)
LCM of 54 and 72 = 2 × 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 54 and 72 = LCM(54, 72) × 2 × 3 = 1296 [Square root of 1296 = √1296 = ±36]
Therefore, 1296 is the required number.

How to Find the LCM of 54 and 72 by Prime Factorization?

To find the LCM of 54 and 72 using prime factorization, we will find the prime factors, (54 = 2 × 3 × 3 × 3) and (72 = 2 × 2 × 2 × 3 × 3). LCM of 54 and 72 is the product of prime factors raised to their respective highest exponent among the numbers 54 and 72.
⇒ LCM of 54, 72 = 2³ × 3³ = 216.