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LCM of 12 and 18

LCM of 12 and 18 is the smallest number among all common multiples of 12 and 18. The first few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (18, 36, 54, 72, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 18 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 12 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 12 and 18?

Answer: LCM of 12 and 18 is 36.

Explanation:

The LCM of two non-zero integers, x(12) and y(18), is the smallest positive integer m(36) that is divisible by both x(12) and y(18) without any remainder.

Methods to Find LCM of 12 and 18

Let's look at the different methods for finding the LCM of 12 and 18.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 12 and 18 by Division Method

To calculate the LCM of 12 and 18 by the division method, we will divide the numbers(12, 18) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 18.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 18. Write this prime number(2) on the left of the given numbers(12 and 18), separated as per the ladder arrangement.
Step 2: If any of the given numbers (12, 18) 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 18 is the product of all prime numbers on the left, i.e. LCM(12, 18) by division method = 2 × 2 × 3 × 3 = 36.

LCM of 12 and 18 by Prime Factorization

Prime factorization of 12 and 18 is (2 × 2 × 3) = 2² × 3¹ and (2 × 3 × 3) = 2¹ × 3² respectively. LCM of 12 and 18 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² = 36.
Hence, the LCM of 12 and 18 by prime factorization is 36.

LCM of 12 and 18 by Listing Multiples

To calculate the LCM of 12 and 18 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, 84, . . . ) and 18 (18, 36, 54, 72, . . . . )
Step 2: The common multiples from the multiples of 12 and 18 are 36, 72, . . .
Step 3: The smallest common multiple of 12 and 18 is 36.

∴ The least common multiple of 12 and 18 = 36.

☛ Also Check:

LCM of 12 and 18 Examples

Example 1: The GCD and LCM of two numbers are 6 and 36 respectively. If one number is 18, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 18 × z
⇒ z = (GCD × LCM)/18
⇒ z = (6 × 36)/18
⇒ z = 12
Therefore, the other number is 12.
Example 2: The product of two numbers is 216. If their GCD is 6, what is their LCM?

Solution:

Given: GCD = 6
product of numbers = 216
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 216/6
Therefore, the LCM is 36.
The probable combination for the given case is LCM(12, 18) = 36.
Example 3: Verify the relationship between GCF and LCM of 12 and 18.

Solution:

The relation between GCF and LCM of 12 and 18 is given as,
LCM(12, 18) × GCF(12, 18) = Product of 12, 18
Prime factorization of 12 and 18 is given as, 12 = (2 × 2 × 3) = 2² × 3¹ and 18 = (2 × 3 × 3) = 2¹ × 3²
LCM(12, 18) = 36
GCF(12, 18) = 6
LHS = LCM(12, 18) × GCF(12, 18) = 36 × 6 = 216
RHS = Product of 12, 18 = 12 × 18 = 216
⇒ LHS = RHS = 216
Hence, verified.

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FAQs on LCM of 12 and 18

What is the LCM of 12 and 18?

The LCM of 12 and 18 is 36. To find the LCM (least common multiple) of 12 and 18, we need to find the multiples of 12 and 18 (multiples of 12 = 12, 24, 36, 48; multiples of 18 = 18, 36, 54, 72) and choose the smallest multiple that is exactly divisible by 12 and 18, i.e., 36.

What is the Least Perfect Square Divisible by 12 and 18?

The least number divisible by 12 and 18 = LCM(12, 18)
LCM of 12 and 18 = 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 12 and 18 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.

If the LCM of 18 and 12 is 36, Find its GCF.

LCM(18, 12) × GCF(18, 12) = 18 × 12
Since the LCM of 18 and 12 = 36
⇒ 36 × GCF(18, 12) = 216
Therefore, the greatest common factor (GCF) = 216/36 = 6.

How to Find the LCM of 12 and 18 by Prime Factorization?

To find the LCM of 12 and 18 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (18 = 2 × 3 × 3). LCM of 12 and 18 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 18.
⇒ LCM of 12, 18 = 2² × 3² = 36.

Which of the following is the LCM of 12 and 18? 36, 10, 12, 2

The value of LCM of 12, 18 is the smallest common multiple of 12 and 18. The number satisfying the given condition is 36.

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