LCM of 12 and 20

LCM of 12 and 20 is the smallest number among all common multiples of 12 and 20. The first few multiples of 12 and 20 are (12, 24, 36, 48, 60, 72, . . . ) and (20, 40, 60, 80, 100, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 20 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 12 and 20 is 60.

Explanation:

The LCM of two non-zero integers, x(12) and y(20), is the smallest positive integer m(60) that is divisible by both x(12) and y(20) without any remainder.

Let's look at the different methods for finding the LCM of 12 and 20.

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

LCM of 12 and 20 by Prime Factorization

Prime factorization of 12 and 20 is (2 × 2 × 3) = 2² × 3¹ and (2 × 2 × 5) = 2² × 5¹ respectively. LCM of 12 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 12 and 20 by prime factorization is 60.

LCM of 12 and 20 by Division Method

To calculate the LCM of 12 and 20 by the division method, we will divide the numbers(12, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 20.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 20. Write this prime number(2) on the left of the given numbers(12 and 20), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 20) 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 20 is the product of all prime numbers on the left, i.e. LCM(12, 20) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 12 and 20 by Listing Multiples

To calculate the LCM of 12 and 20 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 20 (20, 40, 60, 80, 100, 120, . . . . )
• Step 2: The common multiples from the multiples of 12 and 20 are 60, 120, . . .
• Step 3: The smallest common multiple of 12 and 20 is 60.

∴ The least common multiple of 12 and 20 = 60.

☛ Also Check:

• LCM of 14 and 42 - 42
• LCM of 14 and 35 - 70
• LCM of 14 and 28 - 28
• LCM of 14 and 24 - 168
• LCM of 14 and 22 - 154
• LCM of 14 and 21 - 42
• LCM of 14 and 20 - 140

FAQs on LCM of 12 and 20

What is the LCM of 12 and 20?

The LCM of 12 and 20 is 60. To find the least common multiple of 12 and 20, we need to find the multiples of 12 and 20 (multiples of 12 = 12, 24, 36, 48 . . . . 60; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 12 and 20, i.e., 60.

What are the Methods to Find LCM of 12 and 20?

The commonly used methods to find the LCM of 12 and 20 are:

• Division Method
• Prime Factorization Method
• Listing Multiples

If the LCM of 20 and 12 is 60, Find its GCF.

LCM(20, 12) × GCF(20, 12) = 20 × 12
Since the LCM of 20 and 12 = 60
⇒ 60 × GCF(20, 12) = 240
Therefore, the GCF (greatest common factor) = 240/60 = 4.

What is the Relation Between GCF and LCM of 12, 20?

The following equation can be used to express the relation between GCF and LCM of 12 and 20, i.e. GCF × LCM = 12 × 20.

Which of the following is the LCM of 12 and 20? 60, 16, 2, 45

The value of LCM of 12, 20 is the smallest common multiple of 12 and 20. The number satisfying the given condition is 60.