LCM of 27 and 81

LCM of 27 and 81 is the smallest number among all common multiples of 27 and 81. The first few multiples of 27 and 81 are (27, 54, 81, 108, 135, 162, . . . ) and (81, 162, 243, 324, 405, . . . ) respectively. There are 3 commonly used methods to find LCM of 27 and 81 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 27 and 81 is 81.

Explanation:

The LCM of two non-zero integers, x(27) and y(81), is the smallest positive integer m(81) that is divisible by both x(27) and y(81) without any remainder.

The methods to find the LCM of 27 and 81 are explained below.

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

LCM of 27 and 81 by Division Method

To calculate the LCM of 27 and 81 by the division method, we will divide the numbers(27, 81) by their prime factors (preferably common). The product of these divisors gives the LCM of 27 and 81.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 27 and 81. Write this prime number(3) on the left of the given numbers(27 and 81), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (27, 81) is a multiple of 3, divide it by 3 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 27 and 81 is the product of all prime numbers on the left, i.e. LCM(27, 81) by division method = 3 × 3 × 3 × 3 = 81.

LCM of 27 and 81 by Listing Multiples

To calculate the LCM of 27 and 81 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 27 (27, 54, 81, 108, 135, 162, . . . ) and 81 (81, 162, 243, 324, 405, . . . . )
• Step 2: The common multiples from the multiples of 27 and 81 are 81, 162, . . .
• Step 3: The smallest common multiple of 27 and 81 is 81.

∴ The least common multiple of 27 and 81 = 81.

LCM of 27 and 81 by Prime Factorization

Prime factorization of 27 and 81 is (3 × 3 × 3) = 3³ and (3 × 3 × 3 × 3) = 3⁴ respectively. LCM of 27 and 81 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3⁴ = 81.
Hence, the LCM of 27 and 81 by prime factorization is 81.

☛ Also Check:

• LCM of 8 and 32 - 32
• LCM of 48 and 72 - 144
• LCM of 24 and 45 - 360
• LCM of 9 and 15 - 45
• LCM of 20 and 35 - 140
• LCM of 16 and 40 - 80
• LCM of 24 and 64 - 192

FAQs on LCM of 27 and 81

What is the LCM of 27 and 81?

The LCM of 27 and 81 is 81. To find the LCM (least common multiple) of 27 and 81, we need to find the multiples of 27 and 81 (multiples of 27 = 27, 54, 81, 108; multiples of 81 = 81, 162, 243, 324) and choose the smallest multiple that is exactly divisible by 27 and 81, i.e., 81.

What are the Methods to Find LCM of 27 and 81?

The commonly used methods to find the LCM of 27 and 81 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

If the LCM of 81 and 27 is 81, Find its GCF.

LCM(81, 27) × GCF(81, 27) = 81 × 27
Since the LCM of 81 and 27 = 81
⇒ 81 × GCF(81, 27) = 2187
Therefore, the greatest common factor (GCF) = 2187/81 = 27.

Which of the following is the LCM of 27 and 81? 27, 15, 11, 81

The value of LCM of 27, 81 is the smallest common multiple of 27 and 81. The number satisfying the given condition is 81.

What is the Least Perfect Square Divisible by 27 and 81?

The least number divisible by 27 and 81 = LCM(27, 81)
LCM of 27 and 81 = 3 × 3 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 27 and 81 = 81 [Square root of 81 = √81 = ±9]
Therefore, 81 is the required number.