LCM of 18 and 56

LCM of 18 and 56 is the smallest number among all common multiples of 18 and 56. The first few multiples of 18 and 56 are (18, 36, 54, 72, . . . ) and (56, 112, 168, 224, 280, 336, 392, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 56 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 18 and 56 is 504.

Explanation:

The LCM of two non-zero integers, x(18) and y(56), is the smallest positive integer m(504) that is divisible by both x(18) and y(56) without any remainder.

The methods to find the LCM of 18 and 56 are explained below.

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

LCM of 18 and 56 by Prime Factorization

Prime factorization of 18 and 56 is (2 × 3 × 3) = 2¹ × 3² and (2 × 2 × 2 × 7) = 2³ × 7¹ respectively. LCM of 18 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² × 7¹ = 504.
Hence, the LCM of 18 and 56 by prime factorization is 504.

LCM of 18 and 56 by Division Method

To calculate the LCM of 18 and 56 by the division method, we will divide the numbers(18, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 56.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 56. Write this prime number(2) on the left of the given numbers(18 and 56), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (18, 56) 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 18 and 56 is the product of all prime numbers on the left, i.e. LCM(18, 56) by division method = 2 × 2 × 2 × 3 × 3 × 7 = 504.

LCM of 18 and 56 by Listing Multiples

To calculate the LCM of 18 and 56 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 18 (18, 36, 54, 72, . . . ) and 56 (56, 112, 168, 224, 280, 336, 392, . . . . )
• Step 2: The common multiples from the multiples of 18 and 56 are 504, 1008, . . .
• Step 3: The smallest common multiple of 18 and 56 is 504.

∴ The least common multiple of 18 and 56 = 504.

☛ Also Check:

• LCM of 14 and 22 - 154
• LCM of 4, 8 and 12 - 24
• LCM of 12 and 13 - 156
• LCM of 75 and 80 - 1200
• LCM of 12 and 18 - 36
• LCM of 10 and 18 - 90
• LCM of 36 and 60 - 180

FAQs on LCM of 18 and 56

What is the LCM of 18 and 56?

The LCM of 18 and 56 is 504. To find the least common multiple of 18 and 56, we need to find the multiples of 18 and 56 (multiples of 18 = 18, 36, 54, 72 . . . . 504; multiples of 56 = 56, 112, 168, 224 . . . . 504) and choose the smallest multiple that is exactly divisible by 18 and 56, i.e., 504.

What are the Methods to Find LCM of 18 and 56?

The commonly used methods to find the LCM of 18 and 56 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

What is the Relation Between GCF and LCM of 18, 56?

The following equation can be used to express the relation between GCF and LCM of 18 and 56, i.e. GCF × LCM = 18 × 56.

What is the Least Perfect Square Divisible by 18 and 56?

The least number divisible by 18 and 56 = LCM(18, 56)
LCM of 18 and 56 = 2 × 2 × 2 × 3 × 3 × 7 [Incomplete pair(s): 2, 7]
⇒ Least perfect square divisible by each 18 and 56 = LCM(18, 56) × 2 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.

If the LCM of 56 and 18 is 504, Find its GCF.

LCM(56, 18) × GCF(56, 18) = 56 × 18
Since the LCM of 56 and 18 = 504
⇒ 504 × GCF(56, 18) = 1008
Therefore, the greatest common factor = 1008/504 = 2.