LCM of 12 and 24

LCM of 12 and 24 is the smallest number among all common multiples of 12 and 24. The first few multiples of 12 and 24 are (12, 24, 36, 48, 60, 72, . . . ) and (24, 48, 72, 96, 120, 144, 168, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 24 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 12 and 24 is 24.

Explanation:

The LCM of two non-zero integers, x(12) and y(24), is the smallest positive integer m(24) that is divisible by both x(12) and y(24) without any remainder.

The methods to find the LCM of 12 and 24 are explained below.

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

LCM of 12 and 24 by Division Method

To calculate the LCM of 12 and 24 by the division method, we will divide the numbers(12, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 24. Write this prime number(2) on the left of the given numbers(12 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 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 12 and 24 is the product of all prime numbers on the left, i.e. LCM(12, 24) by division method = 2 × 2 × 2 × 3 = 24.

LCM of 12 and 24 by Listing Multiples

To calculate the LCM of 12 and 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 24 (24, 48, 72, 96, 120, 144, 168, . . . . )
• Step 2: The common multiples from the multiples of 12 and 24 are 24, 48, . . .
• Step 3: The smallest common multiple of 12 and 24 is 24.

∴ The least common multiple of 12 and 24 = 24.

LCM of 12 and 24 by Prime Factorization

Prime factorization of 12 and 24 is (2 × 2 × 3) = 2² × 3¹ and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 12 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ = 24.
Hence, the LCM of 12 and 24 by prime factorization is 24.

☛ Also Check:

• LCM of 125 and 175 - 875
• LCM of 120 and 90 - 360
• LCM of 120 and 180 - 360
• LCM of 120 and 160 - 480
• LCM of 120 and 150 - 600
• LCM of 120 and 144 - 720
• LCM of 12 and 60 - 60

FAQs on LCM of 12 and 24

What is the LCM of 12 and 24?

The LCM of 12 and 24 is 24. To find the LCM of 12 and 24, we need to find the multiples of 12 and 24 (multiples of 12 = 12, 24, 36, 48; multiples of 24 = 24, 48, 72, 96) and choose the smallest multiple that is exactly divisible by 12 and 24, i.e., 24.

What are the Methods to Find LCM of 12 and 24?

The commonly used methods to find the LCM of 12 and 24 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

What is the Relation Between GCF and LCM of 12, 24?

The following equation can be used to express the relation between GCF and LCM of 12 and 24, i.e. GCF × LCM = 12 × 24.

If the LCM of 24 and 12 is 24, Find its GCF.

LCM(24, 12) × GCF(24, 12) = 24 × 12
Since the LCM of 24 and 12 = 24
⇒ 24 × GCF(24, 12) = 288
Therefore, the greatest common factor = 288/24 = 12.

How to Find the LCM of 12 and 24 by Prime Factorization?

To find the LCM of 12 and 24 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (24 = 2 × 2 × 2 × 3). LCM of 12 and 24 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 24.
⇒ LCM of 12, 24 = 2³ × 3¹ = 24.