LCM of 45 and 54

LCM of 45 and 54 is the smallest number among all common multiples of 45 and 54. The first few multiples of 45 and 54 are (45, 90, 135, 180, 225, 270, . . . ) and (54, 108, 162, 216, 270, 324, . . . ) respectively. There are 3 commonly used methods to find LCM of 45 and 54 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 45 and 54 is 270.

Explanation:

The LCM of two non-zero integers, x(45) and y(54), is the smallest positive integer m(270) that is divisible by both x(45) and y(54) without any remainder.

Let's look at the different methods for finding the LCM of 45 and 54.

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

LCM of 45 and 54 by Division Method

To calculate the LCM of 45 and 54 by the division method, we will divide the numbers(45, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 45 and 54.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 45 and 54. Write this prime number(2) on the left of the given numbers(45 and 54), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (45, 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 45 and 54 is the product of all prime numbers on the left, i.e. LCM(45, 54) by division method = 2 × 3 × 3 × 3 × 5 = 270.

LCM of 45 and 54 by Prime Factorization

Prime factorization of 45 and 54 is (3 × 3 × 5) = 3² × 5¹ and (2 × 3 × 3 × 3) = 2¹ × 3³ respectively. LCM of 45 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 45 and 54 by prime factorization is 270.

LCM of 45 and 54 by Listing Multiples

To calculate the LCM of 45 and 54 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 45 (45, 90, 135, 180, 225, 270, . . . ) and 54 (54, 108, 162, 216, 270, 324, . . . . )
• Step 2: The common multiples from the multiples of 45 and 54 are 270, 540, . . .
• Step 3: The smallest common multiple of 45 and 54 is 270.

∴ The least common multiple of 45 and 54 = 270.

☛ Also Check:

• LCM of 2, 3 and 4 - 12
• LCM of 4 and 7 - 28
• LCM of 30 and 60 - 60
• LCM of 9 and 12 - 36
• LCM of 5 and 15 - 15
• LCM of 24 and 64 - 192
• LCM of 25 and 75 - 75

FAQs on LCM of 45 and 54

What is the LCM of 45 and 54?

The LCM of 45 and 54 is 270. To find the least common multiple of 45 and 54, we need to find the multiples of 45 and 54 (multiples of 45 = 45, 90, 135, 180 . . . . 270; multiples of 54 = 54, 108, 162, 216 . . . . 270) and choose the smallest multiple that is exactly divisible by 45 and 54, i.e., 270.

If the LCM of 54 and 45 is 270, Find its GCF.

LCM(54, 45) × GCF(54, 45) = 54 × 45
Since the LCM of 54 and 45 = 270
⇒ 270 × GCF(54, 45) = 2430
Therefore, the greatest common factor (GCF) = 2430/270 = 9.

What is the Least Perfect Square Divisible by 45 and 54?

The least number divisible by 45 and 54 = LCM(45, 54)
LCM of 45 and 54 = 2 × 3 × 3 × 3 × 5 [Incomplete pair(s): 2, 3, 5]
⇒ Least perfect square divisible by each 45 and 54 = LCM(45, 54) × 2 × 3 × 5 = 8100 [Square root of 8100 = √8100 = ±90]
Therefore, 8100 is the required number.

How to Find the LCM of 45 and 54 by Prime Factorization?

To find the LCM of 45 and 54 using prime factorization, we will find the prime factors, (45 = 3 × 3 × 5) and (54 = 2 × 3 × 3 × 3). LCM of 45 and 54 is the product of prime factors raised to their respective highest exponent among the numbers 45 and 54.
⇒ LCM of 45, 54 = 2¹ × 3³ × 5¹ = 270.

Which of the following is the LCM of 45 and 54? 21, 270, 42, 28

The value of LCM of 45, 54 is the smallest common multiple of 45 and 54. The number satisfying the given condition is 270.