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LCM of 27 and 63

LCM of 27 and 63 is the smallest number among all common multiples of 27 and 63. The first few multiples of 27 and 63 are (27, 54, 81, 108, 135, . . . ) and (63, 126, 189, 252, 315, 378, 441, . . . ) respectively. There are 3 commonly used methods to find LCM of 27 and 63 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 27 and 63
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 27 and 63?

Answer: LCM of 27 and 63 is 189.

Explanation:

The LCM of two non-zero integers, x(27) and y(63), is the smallest positive integer m(189) that is divisible by both x(27) and y(63) without any remainder.

Methods to Find LCM of 27 and 63

Let's look at the different methods for finding the LCM of 27 and 63.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 27 and 63 by Listing Multiples

To calculate the LCM of 27 and 63 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 27 (27, 54, 81, 108, 135, . . . ) and 63 (63, 126, 189, 252, 315, 378, 441, . . . . )
Step 2: The common multiples from the multiples of 27 and 63 are 189, 378, . . .
Step 3: The smallest common multiple of 27 and 63 is 189.

∴ The least common multiple of 27 and 63 = 189.

LCM of 27 and 63 by Prime Factorization

Prime factorization of 27 and 63 is (3 × 3 × 3) = 3³ and (3 × 3 × 7) = 3² × 7¹ respectively. LCM of 27 and 63 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3³ × 7¹ = 189.
Hence, the LCM of 27 and 63 by prime factorization is 189.

LCM of 27 and 63 by Division Method

To calculate the LCM of 27 and 63 by the division method, we will divide the numbers(27, 63) by their prime factors (preferably common). The product of these divisors gives the LCM of 27 and 63.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 27 and 63. Write this prime number(3) on the left of the given numbers(27 and 63), separated as per the ladder arrangement.
Step 2: If any of the given numbers (27, 63) is a multiple of 3, divide it by 3 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 27 and 63 is the product of all prime numbers on the left, i.e. LCM(27, 63) by division method = 3 × 3 × 3 × 7 = 189.

☛ Also Check:

LCM of 27 and 63 Examples

Example 1: The product of two numbers is 1701. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 1701
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1701/9
Therefore, the LCM is 189.
The probable combination for the given case is LCM(27, 63) = 189.
Example 2: The GCD and LCM of two numbers are 9 and 189 respectively. If one number is 63, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 63 × p
⇒ p = (GCD × LCM)/63
⇒ p = (9 × 189)/63
⇒ p = 27
Therefore, the other number is 27.
Example 3: Verify the relationship between GCF and LCM of 27 and 63.

Solution:

The relation between GCF and LCM of 27 and 63 is given as,
LCM(27, 63) × GCF(27, 63) = Product of 27, 63
Prime factorization of 27 and 63 is given as, 27 = (3 × 3 × 3) = 3³ and 63 = (3 × 3 × 7) = 3² × 7¹
LCM(27, 63) = 189
GCF(27, 63) = 9
LHS = LCM(27, 63) × GCF(27, 63) = 189 × 9 = 1701
RHS = Product of 27, 63 = 27 × 63 = 1701
⇒ LHS = RHS = 1701
Hence, verified.

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FAQs on LCM of 27 and 63

What is the LCM of 27 and 63?

The LCM of 27 and 63 is 189. To find the LCM of 27 and 63, we need to find the multiples of 27 and 63 (multiples of 27 = 27, 54, 81, 108 . . . . 189; multiples of 63 = 63, 126, 189, 252) and choose the smallest multiple that is exactly divisible by 27 and 63, i.e., 189.

How to Find the LCM of 27 and 63 by Prime Factorization?

To find the LCM of 27 and 63 using prime factorization, we will find the prime factors, (27 = 3 × 3 × 3) and (63 = 3 × 3 × 7). LCM of 27 and 63 is the product of prime factors raised to their respective highest exponent among the numbers 27 and 63.
⇒ LCM of 27, 63 = 3³ × 7¹ = 189.

What is the Relation Between GCF and LCM of 27, 63?

The following equation can be used to express the relation between GCF and LCM of 27 and 63, i.e. GCF × LCM = 27 × 63.

If the LCM of 63 and 27 is 189, Find its GCF.

LCM(63, 27) × GCF(63, 27) = 63 × 27
Since the LCM of 63 and 27 = 189
⇒ 189 × GCF(63, 27) = 1701
Therefore, the GCF (greatest common factor) = 1701/189 = 9.

Which of the following is the LCM of 27 and 63? 5, 27, 189, 50

The value of LCM of 27, 63 is the smallest common multiple of 27 and 63. The number satisfying the given condition is 189.

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