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LCM of 12 and 28

LCM of 12 and 28 is the smallest number among all common multiples of 12 and 28. The first few multiples of 12 and 28 are (12, 24, 36, 48, 60, 72, . . . ) and (28, 56, 84, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 28 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 12 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 12 and 28?

Answer: LCM of 12 and 28 is 84.

Explanation:

The LCM of two non-zero integers, x(12) and y(28), is the smallest positive integer m(84) that is divisible by both x(12) and y(28) without any remainder.

Methods to Find LCM of 12 and 28

The methods to find the LCM of 12 and 28 are explained below.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 12 and 28 by Listing Multiples

To calculate the LCM of 12 and 28 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 28 (28, 56, 84, 112, . . . . )
Step 2: The common multiples from the multiples of 12 and 28 are 84, 168, . . .
Step 3: The smallest common multiple of 12 and 28 is 84.

∴ The least common multiple of 12 and 28 = 84.

LCM of 12 and 28 by Prime Factorization

Prime factorization of 12 and 28 is (2 × 2 × 3) = 2² × 3¹ and (2 × 2 × 7) = 2² × 7¹ respectively. LCM of 12 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 7¹ = 84.
Hence, the LCM of 12 and 28 by prime factorization is 84.

LCM of 12 and 28 by Division Method

To calculate the LCM of 12 and 28 by the division method, we will divide the numbers(12, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 28.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 28. Write this prime number(2) on the left of the given numbers(12 and 28), separated as per the ladder arrangement.
Step 2: If any of the given numbers (12, 28) 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 28 is the product of all prime numbers on the left, i.e. LCM(12, 28) by division method = 2 × 2 × 3 × 7 = 84.

☛ Also Check:

LCM of 12 and 28 Examples

Example 1: Verify the relationship between GCF and LCM of 12 and 28.

Solution:

The relation between GCF and LCM of 12 and 28 is given as,
LCM(12, 28) × GCF(12, 28) = Product of 12, 28
Prime factorization of 12 and 28 is given as, 12 = (2 × 2 × 3) = 2² × 3¹ and 28 = (2 × 2 × 7) = 2² × 7¹
LCM(12, 28) = 84
GCF(12, 28) = 4
LHS = LCM(12, 28) × GCF(12, 28) = 84 × 4 = 336
RHS = Product of 12, 28 = 12 × 28 = 336
⇒ LHS = RHS = 336
Hence, verified.
Example 2: The product of two numbers is 336. If their GCD is 4, what is their LCM?

Solution:

Given: GCD = 4
product of numbers = 336
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 336/4
Therefore, the LCM is 84.
The probable combination for the given case is LCM(12, 28) = 84.
Example 3: The GCD and LCM of two numbers are 4 and 84 respectively. If one number is 28, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 28 × p
⇒ p = (GCD × LCM)/28
⇒ p = (4 × 84)/28
⇒ p = 12
Therefore, the other number is 12.

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FAQs on LCM of 12 and 28

What is the LCM of 12 and 28?

The LCM of 12 and 28 is 84. To find the least common multiple (LCM) of 12 and 28, we need to find the multiples of 12 and 28 (multiples of 12 = 12, 24, 36, 48 . . . . 84; multiples of 28 = 28, 56, 84, 112) and choose the smallest multiple that is exactly divisible by 12 and 28, i.e., 84.

If the LCM of 28 and 12 is 84, Find its GCF.

LCM(28, 12) × GCF(28, 12) = 28 × 12
Since the LCM of 28 and 12 = 84
⇒ 84 × GCF(28, 12) = 336
Therefore, the greatest common factor (GCF) = 336/84 = 4.

What are the Methods to Find LCM of 12 and 28?

The commonly used methods to find the LCM of 12 and 28 are:

Division Method
Prime Factorization Method
Listing Multiples

What is the Relation Between GCF and LCM of 12, 28?

The following equation can be used to express the relation between GCF and LCM of 12 and 28, i.e. GCF × LCM = 12 × 28.

What is the Least Perfect Square Divisible by 12 and 28?

The least number divisible by 12 and 28 = LCM(12, 28)
LCM of 12 and 28 = 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 12 and 28 = LCM(12, 28) × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.

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