LCM of 54 and 90

LCM of 54 and 90 is the smallest number among all common multiples of 54 and 90. The first few multiples of 54 and 90 are (54, 108, 162, 216, . . . ) and (90, 180, 270, 360, 450, . . . ) respectively. There are 3 commonly used methods to find LCM of 54 and 90 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 54 and 90 is 270.

Explanation:

The LCM of two non-zero integers, x(54) and y(90), is the smallest positive integer m(270) that is divisible by both x(54) and y(90) without any remainder.

Let's look at the different methods for finding the LCM of 54 and 90.

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

LCM of 54 and 90 by Prime Factorization

Prime factorization of 54 and 90 is (2 × 3 × 3 × 3) = 2¹ × 3³ and (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ respectively. LCM of 54 and 90 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3³ × 5¹ = 270.
Hence, the LCM of 54 and 90 by prime factorization is 270.

LCM of 54 and 90 by Division Method

To calculate the LCM of 54 and 90 by the division method, we will divide the numbers(54, 90) by their prime factors (preferably common). The product of these divisors gives the LCM of 54 and 90.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 54 and 90. Write this prime number(2) on the left of the given numbers(54 and 90), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (54, 90) 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 54 and 90 is the product of all prime numbers on the left, i.e. LCM(54, 90) by division method = 2 × 3 × 3 × 3 × 5 = 270.

LCM of 54 and 90 by Listing Multiples

To calculate the LCM of 54 and 90 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 54 (54, 108, 162, 216, . . . ) and 90 (90, 180, 270, 360, 450, . . . . )
• Step 2: The common multiples from the multiples of 54 and 90 are 270, 540, . . .
• Step 3: The smallest common multiple of 54 and 90 is 270.

∴ The least common multiple of 54 and 90 = 270.

☛ Also Check:

• LCM of 42 and 63 - 126
• LCM of 30 and 54 - 270
• LCM of 18, 24 and 30 - 360
• LCM of 9 and 11 - 99
• LCM of 24 and 42 - 168
• LCM of 3 and 4 - 12
• LCM of 8, 12 and 15 - 120

FAQs on LCM of 54 and 90

What is the LCM of 54 and 90?

The LCM of 54 and 90 is 270. To find the LCM of 54 and 90, we need to find the multiples of 54 and 90 (multiples of 54 = 54, 108, 162, 216 . . . . 270; multiples of 90 = 90, 180, 270, 360) and choose the smallest multiple that is exactly divisible by 54 and 90, i.e., 270.

What are the Methods to Find LCM of 54 and 90?

The commonly used methods to find the LCM of 54 and 90 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

If the LCM of 90 and 54 is 270, Find its GCF.

LCM(90, 54) × GCF(90, 54) = 90 × 54
Since the LCM of 90 and 54 = 270
⇒ 270 × GCF(90, 54) = 4860
Therefore, the greatest common factor = 4860/270 = 18.

Which of the following is the LCM of 54 and 90? 270, 28, 45, 5

The value of LCM of 54, 90 is the smallest common multiple of 54 and 90. The number satisfying the given condition is 270.

What is the Relation Between GCF and LCM of 54, 90?

The following equation can be used to express the relation between GCF and LCM of 54 and 90, i.e. GCF × LCM = 54 × 90.