LCM of 6 and 24

LCM of 6 and 24 is the smallest number among all common multiples of 6 and 24. The first few multiples of 6 and 24 are (6, 12, 18, 24, . . . ) and (24, 48, 72, 96, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 24 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 6 and 24 is 24.

Explanation:

The LCM of two non-zero integers, x(6) and y(24), is the smallest positive integer m(24) that is divisible by both x(6) and y(24) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 24.

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

LCM of 6 and 24 by Listing Multiples

To calculate the LCM of 6 and 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, . . . ) and 24 (24, 48, 72, 96, 120, . . . . )
• Step 2: The common multiples from the multiples of 6 and 24 are 24, 48, . . .
• Step 3: The smallest common multiple of 6 and 24 is 24.

∴ The least common multiple of 6 and 24 = 24.

LCM of 6 and 24 by Division Method

To calculate the LCM of 6 and 24 by the division method, we will divide the numbers(6, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 24. Write this prime number(2) on the left of the given numbers(6 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 24) 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 6 and 24 is the product of all prime numbers on the left, i.e. LCM(6, 24) by division method = 2 × 2 × 2 × 3 = 24.

LCM of 6 and 24 by Prime Factorization

Prime factorization of 6 and 24 is (2 × 3) = 2¹ × 3¹ and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 6 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ = 24.
Hence, the LCM of 6 and 24 by prime factorization is 24.

☛ Also Check:

• LCM of 12 and 30 - 60
• LCM of 25 and 75 - 75
• LCM of 3 and 10 - 30
• LCM of 18, 24 and 36 - 72
• LCM of 3, 4 and 5 - 60
• LCM of 12 and 42 - 84
• LCM of 36, 42 and 72 - 504

FAQs on LCM of 6 and 24

What is the LCM of 6 and 24?

The LCM of 6 and 24 is 24. To find the least common multiple of 6 and 24, we need to find the multiples of 6 and 24 (multiples of 6 = 6, 12, 18, 24; multiples of 24 = 24, 48, 72, 96) and choose the smallest multiple that is exactly divisible by 6 and 24, i.e., 24.

What is the Relation Between GCF and LCM of 6, 24?

The following equation can be used to express the relation between GCF and LCM of 6 and 24, i.e. GCF × LCM = 6 × 24.

Which of the following is the LCM of 6 and 24? 35, 50, 24, 40

The value of LCM of 6, 24 is the smallest common multiple of 6 and 24. The number satisfying the given condition is 24.

If the LCM of 24 and 6 is 24, Find its GCF.

LCM(24, 6) × GCF(24, 6) = 24 × 6
Since the LCM of 24 and 6 = 24
⇒ 24 × GCF(24, 6) = 144
Therefore, the greatest common factor (GCF) = 144/24 = 6.

How to Find the LCM of 6 and 24 by Prime Factorization?

To find the LCM of 6 and 24 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (24 = 2 × 2 × 2 × 3). LCM of 6 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 24.
⇒ LCM of 6, 24 = 2³ × 3¹ = 24.