LCM of 3 and 27

LCM of 3 and 27 is the smallest number among all common multiples of 3 and 27. The first few multiples of 3 and 27 are (3, 6, 9, 12, . . . ) and (27, 54, 81, 108, 135, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 27 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 3 and 27 is 27.

Explanation:

The LCM of two non-zero integers, x(3) and y(27), is the smallest positive integer m(27) that is divisible by both x(3) and y(27) without any remainder.

Let's look at the different methods for finding the LCM of 3 and 27.

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

LCM of 3 and 27 by Listing Multiples

To calculate the LCM of 3 and 27 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 3 (3, 6, 9, 12, . . . ) and 27 (27, 54, 81, 108, 135, . . . . )
• Step 2: The common multiples from the multiples of 3 and 27 are 27, 54, . . .
• Step 3: The smallest common multiple of 3 and 27 is 27.

∴ The least common multiple of 3 and 27 = 27.

LCM of 3 and 27 by Prime Factorization

Prime factorization of 3 and 27 is (3) = 3¹ and (3 × 3 × 3) = 3³ respectively. LCM of 3 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3³ = 27.
Hence, the LCM of 3 and 27 by prime factorization is 27.

LCM of 3 and 27 by Division Method

To calculate the LCM of 3 and 27 by the division method, we will divide the numbers(3, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 27.

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

☛ Also Check:

• LCM of 36 and 84 - 252
• LCM of 6, 8 and 15 - 120
• LCM of 5 and 7 - 35
• LCM of 36 and 45 - 180
• LCM of 16 and 20 - 80
• LCM of 45 and 120 - 360
• LCM of 28 and 42 - 84

FAQs on LCM of 3 and 27

What is the LCM of 3 and 27?

The LCM of 3 and 27 is 27. To find the LCM (least common multiple) of 3 and 27, we need to find the multiples of 3 and 27 (multiples of 3 = 3, 6, 9, 12 . . . . 27; multiples of 27 = 27, 54, 81, 108) and choose the smallest multiple that is exactly divisible by 3 and 27, i.e., 27.

If the LCM of 27 and 3 is 27, Find its GCF.

LCM(27, 3) × GCF(27, 3) = 27 × 3
Since the LCM of 27 and 3 = 27
⇒ 27 × GCF(27, 3) = 81
Therefore, the greatest common factor (GCF) = 81/27 = 3.

What is the Relation Between GCF and LCM of 3, 27?

The following equation can be used to express the relation between GCF and LCM of 3 and 27, i.e. GCF × LCM = 3 × 27.

What are the Methods to Find LCM of 3 and 27?

The commonly used methods to find the LCM of 3 and 27 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 3 and 27?

The least number divisible by 3 and 27 = LCM(3, 27)
LCM of 3 and 27 = 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 3 and 27 = LCM(3, 27) × 3 = 81 [Square root of 81 = √81 = ±9]
Therefore, 81 is the required number.