LCM of 54 and 60

LCM of 54 and 60 is the smallest number among all common multiples of 54 and 60. The first few multiples of 54 and 60 are (54, 108, 162, 216, 270, 324, . . . ) and (60, 120, 180, 240, . . . ) respectively. There are 3 commonly used methods to find LCM of 54 and 60 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 54 and 60 is 540.

Explanation:

The LCM of two non-zero integers, x(54) and y(60), is the smallest positive integer m(540) that is divisible by both x(54) and y(60) without any remainder.

Let's look at the different methods for finding the LCM of 54 and 60.

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

LCM of 54 and 60 by Prime Factorization

Prime factorization of 54 and 60 is (2 × 3 × 3 × 3) = 2¹ × 3³ and (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ respectively. LCM of 54 and 60 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3³ × 5¹ = 540.
Hence, the LCM of 54 and 60 by prime factorization is 540.

LCM of 54 and 60 by Listing Multiples

To calculate the LCM of 54 and 60 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 60 (60, 120, 180, 240, . . . . )
• Step 2: The common multiples from the multiples of 54 and 60 are 540, 1080, . . .
• Step 3: The smallest common multiple of 54 and 60 is 540.

∴ The least common multiple of 54 and 60 = 540.

LCM of 54 and 60 by Division Method

To calculate the LCM of 54 and 60 by the division method, we will divide the numbers(54, 60) by their prime factors (preferably common). The product of these divisors gives the LCM of 54 and 60.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 54 and 60. Write this prime number(2) on the left of the given numbers(54 and 60), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (54, 60) 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 60 is the product of all prime numbers on the left, i.e. LCM(54, 60) by division method = 2 × 2 × 3 × 3 × 3 × 5 = 540.

☛ Also Check:

• LCM of 4 and 10 - 20
• LCM of 36 and 72 - 72
• LCM of 56 and 70 - 280
• LCM of 40, 48 and 45 - 720
• LCM of 8, 9 and 12 - 72
• LCM of 4 and 20 - 20
• LCM of 30, 36 and 40 - 360

FAQs on LCM of 54 and 60

What is the LCM of 54 and 60?

The LCM of 54 and 60 is 540. To find the least common multiple (LCM) of 54 and 60, we need to find the multiples of 54 and 60 (multiples of 54 = 54, 108, 162, 216 . . . . 540; multiples of 60 = 60, 120, 180, 240 . . . . 540) and choose the smallest multiple that is exactly divisible by 54 and 60, i.e., 540.

What are the Methods to Find LCM of 54 and 60?

The commonly used methods to find the LCM of 54 and 60 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

What is the Least Perfect Square Divisible by 54 and 60?

The least number divisible by 54 and 60 = LCM(54, 60)
LCM of 54 and 60 = 2 × 2 × 3 × 3 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 54 and 60 = LCM(54, 60) × 3 × 5 = 8100 [Square root of 8100 = √8100 = ±90]
Therefore, 8100 is the required number.

If the LCM of 60 and 54 is 540, Find its GCF.

LCM(60, 54) × GCF(60, 54) = 60 × 54
Since the LCM of 60 and 54 = 540
⇒ 540 × GCF(60, 54) = 3240
Therefore, the GCF (greatest common factor) = 3240/540 = 6.

How to Find the LCM of 54 and 60 by Prime Factorization?

To find the LCM of 54 and 60 using prime factorization, we will find the prime factors, (54 = 2 × 3 × 3 × 3) and (60 = 2 × 2 × 3 × 5). LCM of 54 and 60 is the product of prime factors raised to their respective highest exponent among the numbers 54 and 60.
⇒ LCM of 54, 60 = 2² × 3³ × 5¹ = 540.