LCM of 30 and 54

LCM of 30 and 54 is the smallest number among all common multiples of 30 and 54. The first few multiples of 30 and 54 are (30, 60, 90, 120, 150, 180, . . . ) and (54, 108, 162, 216, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 54 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 30 and 54 is 270.

Explanation:

The LCM of two non-zero integers, x(30) and y(54), is the smallest positive integer m(270) that is divisible by both x(30) and y(54) without any remainder.

The methods to find the LCM of 30 and 54 are explained below.

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

LCM of 30 and 54 by Prime Factorization

Prime factorization of 30 and 54 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (2 × 3 × 3 × 3) = 2¹ × 3³ respectively. LCM of 30 and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3³ × 5¹ = 270.
Hence, the LCM of 30 and 54 by prime factorization is 270.

LCM of 30 and 54 by Listing Multiples

To calculate the LCM of 30 and 54 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 30 (30, 60, 90, 120, 150, 180, . . . ) and 54 (54, 108, 162, 216, . . . . )
• Step 2: The common multiples from the multiples of 30 and 54 are 270, 540, . . .
• Step 3: The smallest common multiple of 30 and 54 is 270.

∴ The least common multiple of 30 and 54 = 270.

LCM of 30 and 54 by Division Method

To calculate the LCM of 30 and 54 by the division method, we will divide the numbers(30, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 54.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 54. Write this prime number(2) on the left of the given numbers(30 and 54), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (30, 54) 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 30 and 54 is the product of all prime numbers on the left, i.e. LCM(30, 54) by division method = 2 × 3 × 3 × 3 × 5 = 270.

☛ Also Check:

• LCM of 14 and 122 - 854
• LCM of 15 and 40 - 120
• LCM of 16 and 48 - 48
• LCM of 2 and 4 - 4
• LCM of 8, 12 and 24 - 24
• LCM of 6, 10 and 12 - 60
• LCM of 2, 4, 6, 8, 10 and 12 - 120

FAQs on LCM of 30 and 54

What is the LCM of 30 and 54?

The LCM of 30 and 54 is 270. To find the LCM of 30 and 54, we need to find the multiples of 30 and 54 (multiples of 30 = 30, 60, 90, 120 . . . . 270; multiples of 54 = 54, 108, 162, 216 . . . . 270) and choose the smallest multiple that is exactly divisible by 30 and 54, i.e., 270.

What is the Relation Between GCF and LCM of 30, 54?

The following equation can be used to express the relation between GCF and LCM of 30 and 54, i.e. GCF × LCM = 30 × 54.

How to Find the LCM of 30 and 54 by Prime Factorization?

To find the LCM of 30 and 54 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (54 = 2 × 3 × 3 × 3). LCM of 30 and 54 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 54.
⇒ LCM of 30, 54 = 2¹ × 3³ × 5¹ = 270.

If the LCM of 54 and 30 is 270, Find its GCF.

LCM(54, 30) × GCF(54, 30) = 54 × 30
Since the LCM of 54 and 30 = 270
⇒ 270 × GCF(54, 30) = 1620
Therefore, the GCF (greatest common factor) = 1620/270 = 6.

What are the Methods to Find LCM of 30 and 54?

The commonly used methods to find the LCM of 30 and 54 are:

• Prime Factorization Method
• Division Method
• Listing Multiples