LCM of 24 and 28

LCM of 24 and 28 is the smallest number among all common multiples of 24 and 28. The first few multiples of 24 and 28 are (24, 48, 72, 96, 120, . . . ) and (28, 56, 84, 112, 140, 168, 196, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 28 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 24 and 28 is 168.

Explanation:

The LCM of two non-zero integers, x(24) and y(28), is the smallest positive integer m(168) that is divisible by both x(24) and y(28) without any remainder.

The methods to find the LCM of 24 and 28 are explained below.

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

LCM of 24 and 28 by Division Method

To calculate the LCM of 24 and 28 by the division method, we will divide the numbers(24, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 28.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 28. Write this prime number(2) on the left of the given numbers(24 and 28), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (24, 28) 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 28 is the product of all prime numbers on the left, i.e. LCM(24, 28) by division method = 2 × 2 × 2 × 3 × 7 = 168.

LCM of 24 and 28 by Listing Multiples

To calculate the LCM of 24 and 28 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 28 (28, 56, 84, 112, 140, 168, 196, . . . . )
• Step 2: The common multiples from the multiples of 24 and 28 are 168, 336, . . .
• Step 3: The smallest common multiple of 24 and 28 is 168.

∴ The least common multiple of 24 and 28 = 168.

LCM of 24 and 28 by Prime Factorization

Prime factorization of 24 and 28 is (2 × 2 × 2 × 3) = 2³ × 3¹ and (2 × 2 × 7) = 2² × 7¹ respectively. LCM of 24 and 28 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 28 by prime factorization is 168.

☛ Also Check:

• LCM of 60 and 84 - 420
• LCM of 14 and 28 - 28
• LCM of 2, 4 and 5 - 20
• LCM of 12, 15 and 21 - 420
• LCM of 8, 12 and 15 - 120
• LCM of 16, 24, 36 and 54 - 432
• LCM of 2, 3 and 4 - 12

FAQs on LCM of 24 and 28

What is the LCM of 24 and 28?

The LCM of 24 and 28 is 168. To find the least common multiple (LCM) of 24 and 28, we need to find the multiples of 24 and 28 (multiples of 24 = 24, 48, 72, 96 . . . . 168; multiples of 28 = 28, 56, 84, 112 . . . . 168) and choose the smallest multiple that is exactly divisible by 24 and 28, i.e., 168.

What are the Methods to Find LCM of 24 and 28?

The commonly used methods to find the LCM of 24 and 28 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 28 and 24 is 168, Find its GCF.

LCM(28, 24) × GCF(28, 24) = 28 × 24
Since the LCM of 28 and 24 = 168
⇒ 168 × GCF(28, 24) = 672
Therefore, the greatest common factor = 672/168 = 4.

Which of the following is the LCM of 24 and 28? 50, 3, 168, 21

The value of LCM of 24, 28 is the smallest common multiple of 24 and 28. The number satisfying the given condition is 168.

How to Find the LCM of 24 and 28 by Prime Factorization?

To find the LCM of 24 and 28 using prime factorization, we will find the prime factors, (24 = 2 × 2 × 2 × 3) and (28 = 2 × 2 × 7). LCM of 24 and 28 is the product of prime factors raised to their respective highest exponent among the numbers 24 and 28.
⇒ LCM of 24, 28 = 2³ × 3¹ × 7¹ = 168.