LCM of 18 and 54

LCM of 18 and 54 is the smallest number among all common multiples of 18 and 54. The first few multiples of 18 and 54 are (18, 36, 54, 72, . . . ) and (54, 108, 162, 216, 270, 324, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 54 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 18 and 54 is 54.

Explanation:

The LCM of two non-zero integers, x(18) and y(54), is the smallest positive integer m(54) that is divisible by both x(18) and y(54) without any remainder.

The methods to find the LCM of 18 and 54 are explained below.

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

LCM of 18 and 54 by Prime Factorization

Prime factorization of 18 and 54 is (2 × 3 × 3) = 2¹ × 3² and (2 × 3 × 3 × 3) = 2¹ × 3³ respectively. LCM of 18 and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3³ = 54.
Hence, the LCM of 18 and 54 by prime factorization is 54.

LCM of 18 and 54 by Division Method

To calculate the LCM of 18 and 54 by the division method, we will divide the numbers(18, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 54.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 54. Write this prime number(2) on the left of the given numbers(18 and 54), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 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 18 and 54 is the product of all prime numbers on the left, i.e. LCM(18, 54) by division method = 2 × 3 × 3 × 3 = 54.

LCM of 18 and 54 by Listing Multiples

To calculate the LCM of 18 and 54 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 18 (18, 36, 54, 72, . . . ) and 54 (54, 108, 162, 216, 270, 324, . . . . )
• Step 2: The common multiples from the multiples of 18 and 54 are 54, 108, . . .
• Step 3: The smallest common multiple of 18 and 54 is 54.

∴ The least common multiple of 18 and 54 = 54.

☛ Also Check:

• LCM of 54 and 72 - 216
• LCM of 7 and 10 - 70
• LCM of 30, 45 and 60 - 180
• LCM of 2, 3 and 5 - 30
• LCM of 148 and 185 - 740
• LCM of 12 and 60 - 60
• LCM of 12, 15, 20 and 54 - 540

FAQs on LCM of 18 and 54

What is the LCM of 18 and 54?

The LCM of 18 and 54 is 54. To find the LCM (least common multiple) of 18 and 54, we need to find the multiples of 18 and 54 (multiples of 18 = 18, 36, 54, 72; multiples of 54 = 54, 108, 162, 216) and choose the smallest multiple that is exactly divisible by 18 and 54, i.e., 54.

What is the Least Perfect Square Divisible by 18 and 54?

The least number divisible by 18 and 54 = LCM(18, 54)
LCM of 18 and 54 = 2 × 3 × 3 × 3 [Incomplete pair(s): 2, 3]
⇒ Least perfect square divisible by each 18 and 54 = LCM(18, 54) × 2 × 3 = 324 [Square root of 324 = √324 = ±18]
Therefore, 324 is the required number.

What are the Methods to Find LCM of 18 and 54?

The commonly used methods to find the LCM of 18 and 54 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

How to Find the LCM of 18 and 54 by Prime Factorization?

To find the LCM of 18 and 54 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (54 = 2 × 3 × 3 × 3). LCM of 18 and 54 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 54.
⇒ LCM of 18, 54 = 2¹ × 3³ = 54.

If the LCM of 54 and 18 is 54, Find its GCF.

LCM(54, 18) × GCF(54, 18) = 54 × 18
Since the LCM of 54 and 18 = 54
⇒ 54 × GCF(54, 18) = 972
Therefore, the greatest common factor = 972/54 = 18.