LCM of 24 and 8

LCM of 24 and 8 is the smallest number among all common multiples of 24 and 8. The first few multiples of 24 and 8 are (24, 48, 72, 96, 120, 144, 168, . . . ) and (8, 16, 24, 32, 40, 48, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 8 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 24 and 8 is 24.

Explanation:

The LCM of two non-zero integers, x(24) and y(8), is the smallest positive integer m(24) that is divisible by both x(24) and y(8) without any remainder.

Let's look at the different methods for finding the LCM of 24 and 8.

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

LCM of 24 and 8 by Listing Multiples

To calculate the LCM of 24 and 8 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, 144, 168, . . . ) and 8 (8, 16, 24, 32, 40, 48, . . . . )
• Step 2: The common multiples from the multiples of 24 and 8 are 24, 48, . . .
• Step 3: The smallest common multiple of 24 and 8 is 24.

∴ The least common multiple of 24 and 8 = 24.

LCM of 24 and 8 by Prime Factorization

Prime factorization of 24 and 8 is (2 × 2 × 2 × 3) = 2³ × 3¹ and (2 × 2 × 2) = 2³ respectively. LCM of 24 and 8 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ = 24.
Hence, the LCM of 24 and 8 by prime factorization is 24.

LCM of 24 and 8 by Division Method

To calculate the LCM of 24 and 8 by the division method, we will divide the numbers(24, 8) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 8.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 8. Write this prime number(2) on the left of the given numbers(24 and 8), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (24, 8) 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 8 is the product of all prime numbers on the left, i.e. LCM(24, 8) by division method = 2 × 2 × 2 × 3 = 24.

☛ Also Check:

• LCM of 2 and 6 - 6
• LCM of 75 and 105 - 525
• LCM of 26 and 169 - 338
• LCM of 8, 12 and 15 - 120
• LCM of 3, 4 and 12 - 12
• LCM of 8 and 42 - 168
• LCM of 4, 5 and 10 - 20

FAQs on LCM of 24 and 8

What is the LCM of 24 and 8?

The LCM of 24 and 8 is 24. To find the LCM (least common multiple) of 24 and 8, we need to find the multiples of 24 and 8 (multiples of 24 = 24, 48, 72, 96; multiples of 8 = 8, 16, 24, 32) and choose the smallest multiple that is exactly divisible by 24 and 8, i.e., 24.

Which of the following is the LCM of 24 and 8? 16, 24, 25, 28

The value of LCM of 24, 8 is the smallest common multiple of 24 and 8. The number satisfying the given condition is 24.

If the LCM of 8 and 24 is 24, Find its GCF.

LCM(8, 24) × GCF(8, 24) = 8 × 24
Since the LCM of 8 and 24 = 24
⇒ 24 × GCF(8, 24) = 192
Therefore, the GCF (greatest common factor) = 192/24 = 8.

What are the Methods to Find LCM of 24 and 8?

The commonly used methods to find the LCM of 24 and 8 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

What is the Relation Between GCF and LCM of 24, 8?

The following equation can be used to express the relation between GCF and LCM of 24 and 8, i.e. GCF × LCM = 24 × 8.