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LCM of 15 and 27

LCM of 15 and 27 is the smallest number among all common multiples of 15 and 27. The first few multiples of 15 and 27 are (15, 30, 45, 60, 75, . . . ) and (27, 54, 81, 108, . . . ) respectively. There are 3 commonly used methods to find LCM of 15 and 27 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 15 and 27
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 15 and 27?

Answer: LCM of 15 and 27 is 135.

Explanation:

The LCM of two non-zero integers, x(15) and y(27), is the smallest positive integer m(135) that is divisible by both x(15) and y(27) without any remainder.

Methods to Find LCM of 15 and 27

Let's look at the different methods for finding the LCM of 15 and 27.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 15 and 27 by Prime Factorization

Prime factorization of 15 and 27 is (3 × 5) = 3¹ × 5¹ and (3 × 3 × 3) = 3³ respectively. LCM of 15 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 3³ × 5¹ = 135.
Hence, the LCM of 15 and 27 by prime factorization is 135.

LCM of 15 and 27 by Division Method

To calculate the LCM of 15 and 27 by the division method, we will divide the numbers(15, 27) by their prime factors (preferably common). The product of these divisors gives the LCM of 15 and 27.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 15 and 27. Write this prime number(3) on the left of the given numbers(15 and 27), separated as per the ladder arrangement.
Step 2: If any of the given numbers (15, 27) 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 15 and 27 is the product of all prime numbers on the left, i.e. LCM(15, 27) by division method = 3 × 3 × 3 × 5 = 135.

LCM of 15 and 27 by Listing Multiples

To calculate the LCM of 15 and 27 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 15 (15, 30, 45, 60, 75, . . . ) and 27 (27, 54, 81, 108, . . . . )
Step 2: The common multiples from the multiples of 15 and 27 are 135, 270, . . .
Step 3: The smallest common multiple of 15 and 27 is 135.

∴ The least common multiple of 15 and 27 = 135.

☛ Also Check:

LCM of 15 and 27 Examples

Example 1: Find the smallest number that is divisible by 15 and 27 exactly.

Solution:

The smallest number that is divisible by 15 and 27 exactly is their LCM.
⇒ Multiples of 15 and 27:
- Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120, 135, . . . .
- Multiples of 27 = 27, 54, 81, 108, 135, 162, 189, . . . .
Therefore, the LCM of 15 and 27 is 135.
Example 2: The GCD and LCM of two numbers are 3 and 135 respectively. If one number is 27, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 27 × p
⇒ p = (GCD × LCM)/27
⇒ p = (3 × 135)/27
⇒ p = 15
Therefore, the other number is 15.
Example 3: The product of two numbers is 405. If their GCD is 3, what is their LCM?

Solution:

Given: GCD = 3
product of numbers = 405
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 405/3
Therefore, the LCM is 135.
The probable combination for the given case is LCM(15, 27) = 135.

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FAQs on LCM of 15 and 27

What is the LCM of 15 and 27?

The LCM of 15 and 27 is 135. To find the least common multiple of 15 and 27, we need to find the multiples of 15 and 27 (multiples of 15 = 15, 30, 45, 60 . . . . 135; multiples of 27 = 27, 54, 81, 108 . . . . 135) and choose the smallest multiple that is exactly divisible by 15 and 27, i.e., 135.

How to Find the LCM of 15 and 27 by Prime Factorization?

To find the LCM of 15 and 27 using prime factorization, we will find the prime factors, (15 = 3 × 5) and (27 = 3 × 3 × 3). LCM of 15 and 27 is the product of prime factors raised to their respective highest exponent among the numbers 15 and 27.
⇒ LCM of 15, 27 = 3³ × 5¹ = 135.

What is the Relation Between GCF and LCM of 15, 27?

The following equation can be used to express the relation between GCF and LCM of 15 and 27, i.e. GCF × LCM = 15 × 27.

Which of the following is the LCM of 15 and 27? 5, 42, 135, 16

The value of LCM of 15, 27 is the smallest common multiple of 15 and 27. The number satisfying the given condition is 135.

If the LCM of 27 and 15 is 135, Find its GCF.

LCM(27, 15) × GCF(27, 15) = 27 × 15
Since the LCM of 27 and 15 = 135
⇒ 135 × GCF(27, 15) = 405
Therefore, the greatest common factor = 405/135 = 3.

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