LCM of 27 and 45

LCM of 27 and 45 is the smallest number among all common multiples of 27 and 45. The first few multiples of 27 and 45 are (27, 54, 81, 108, . . . ) and (45, 90, 135, 180, 225, 270, 315, . . . ) respectively. There are 3 commonly used methods to find LCM of 27 and 45 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 27 and 45 is 135.

Explanation:

The LCM of two non-zero integers, x(27) and y(45), is the smallest positive integer m(135) that is divisible by both x(27) and y(45) without any remainder.

Let's look at the different methods for finding the LCM of 27 and 45.

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

LCM of 27 and 45 by Prime Factorization

Prime factorization of 27 and 45 is (3 × 3 × 3) = 3³ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 27 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3³ × 5¹ = 135.
Hence, the LCM of 27 and 45 by prime factorization is 135.

LCM of 27 and 45 by Division Method

To calculate the LCM of 27 and 45 by the division method, we will divide the numbers(27, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 27 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 27 and 45. Write this prime number(3) on the left of the given numbers(27 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (27, 45) 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 45 is the product of all prime numbers on the left, i.e. LCM(27, 45) by division method = 3 × 3 × 3 × 5 = 135.

LCM of 27 and 45 by Listing Multiples

To calculate the LCM of 27 and 45 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, . . . ) and 45 (45, 90, 135, 180, 225, 270, 315, . . . . )
• Step 2: The common multiples from the multiples of 27 and 45 are 135, 270, . . .
• Step 3: The smallest common multiple of 27 and 45 is 135.

∴ The least common multiple of 27 and 45 = 135.

☛ Also Check:

• LCM of 21 and 24 - 168
• LCM of 32 and 36 - 288
• LCM of 105 and 195 - 1365
• LCM of 150 and 180 - 900
• LCM of 16 and 64 - 64
• LCM of 2923 and 3239 - 119843
• LCM of 70 and 90 - 630

FAQs on LCM of 27 and 45

What is the LCM of 27 and 45?

The LCM of 27 and 45 is 135. To find the least common multiple of 27 and 45, we need to find the multiples of 27 and 45 (multiples of 27 = 27, 54, 81, 108 . . . . 135; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 27 and 45, i.e., 135.

What are the Methods to Find LCM of 27 and 45?

The commonly used methods to find the LCM of 27 and 45 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

How to Find the LCM of 27 and 45 by Prime Factorization?

To find the LCM of 27 and 45 using prime factorization, we will find the prime factors, (27 = 3 × 3 × 3) and (45 = 3 × 3 × 5). LCM of 27 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 27 and 45.
⇒ LCM of 27, 45 = 3³ × 5¹ = 135.

If the LCM of 45 and 27 is 135, Find its GCF.

LCM(45, 27) × GCF(45, 27) = 45 × 27
Since the LCM of 45 and 27 = 135
⇒ 135 × GCF(45, 27) = 1215
Therefore, the greatest common factor = 1215/135 = 9.

What is the Relation Between GCF and LCM of 27, 45?

The following equation can be used to express the relation between GCF and LCM of 27 and 45, i.e. GCF × LCM = 27 × 45.