LCM of 24 and 56

LCM of 24 and 56 is the smallest number among all common multiples of 24 and 56. The first few multiples of 24 and 56 are (24, 48, 72, 96, 120, . . . ) and (56, 112, 168, 224, 280, 336, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 56 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 24 and 56 is 168.

Explanation:

The LCM of two non-zero integers, x(24) and y(56), is the smallest positive integer m(168) that is divisible by both x(24) and y(56) without any remainder.

The methods to find the LCM of 24 and 56 are explained below.

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

LCM of 24 and 56 by Division Method

To calculate the LCM of 24 and 56 by the division method, we will divide the numbers(24, 56) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 56.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 56. Write this prime number(2) on the left of the given numbers(24 and 56), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (24, 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 24 and 56 is the product of all prime numbers on the left, i.e. LCM(24, 56) by division method = 2 × 2 × 2 × 3 × 7 = 168.

LCM of 24 and 56 by Listing Multiples

To calculate the LCM of 24 and 56 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 24 (24, 48, 72, 96, 120, . . . ) and 56 (56, 112, 168, 224, 280, 336, . . . . )
• Step 2: The common multiples from the multiples of 24 and 56 are 168, 336, . . .
• Step 3: The smallest common multiple of 24 and 56 is 168.

∴ The least common multiple of 24 and 56 = 168.

LCM of 24 and 56 by Prime Factorization

Prime factorization of 24 and 56 is (2 × 2 × 2 × 3) = 2³ × 3¹ and (2 × 2 × 2 × 7) = 2³ × 7¹ respectively. LCM of 24 and 56 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 7¹ = 168.
Hence, the LCM of 24 and 56 by prime factorization is 168.

☛ Also Check:

• LCM of 15, 25, 40 and 75 - 600
• LCM of 2, 4, 6, 8 and 10 - 120
• LCM of 24 and 26 - 312
• LCM of 35 and 70 - 70
• LCM of 3 and 11 - 33
• LCM of 32 and 36 - 288
• LCM of 6, 7 and 9 - 126

FAQs on LCM of 24 and 56

What is the LCM of 24 and 56?

The LCM of 24 and 56 is 168. To find the least common multiple of 24 and 56, we need to find the multiples of 24 and 56 (multiples of 24 = 24, 48, 72, 96 . . . . 168; multiples of 56 = 56, 112, 168, 224) and choose the smallest multiple that is exactly divisible by 24 and 56, i.e., 168.

Which of the following is the LCM of 24 and 56? 15, 25, 12, 168

The value of LCM of 24, 56 is the smallest common multiple of 24 and 56. The number satisfying the given condition is 168.

What are the Methods to Find LCM of 24 and 56?

The commonly used methods to find the LCM of 24 and 56 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

What is the Least Perfect Square Divisible by 24 and 56?

The least number divisible by 24 and 56 = LCM(24, 56)
LCM of 24 and 56 = 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 24 and 56 = LCM(24, 56) × 2 × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.

If the LCM of 56 and 24 is 168, Find its GCF.

LCM(56, 24) × GCF(56, 24) = 56 × 24
Since the LCM of 56 and 24 = 168
⇒ 168 × GCF(56, 24) = 1344
Therefore, the greatest common factor = 1344/168 = 8.