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LCM of 18 and 81

LCM of 18 and 81 is the smallest number among all common multiples of 18 and 81. The first few multiples of 18 and 81 are (18, 36, 54, 72, 90, . . . ) and (81, 162, 243, 324, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 81 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 18 and 81
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 18 and 81?

Answer: LCM of 18 and 81 is 162.

Explanation:

The LCM of two non-zero integers, x(18) and y(81), is the smallest positive integer m(162) that is divisible by both x(18) and y(81) without any remainder.

Methods to Find LCM of 18 and 81

Let's look at the different methods for finding the LCM of 18 and 81.

By Listing Multiples
By Prime Factorization Method
By Division Method

LCM of 18 and 81 by Listing Multiples

To calculate the LCM of 18 and 81 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 18 (18, 36, 54, 72, 90, . . . ) and 81 (81, 162, 243, 324, . . . . )
Step 2: The common multiples from the multiples of 18 and 81 are 162, 324, . . .
Step 3: The smallest common multiple of 18 and 81 is 162.

∴ The least common multiple of 18 and 81 = 162.

LCM of 18 and 81 by Prime Factorization

Prime factorization of 18 and 81 is (2 × 3 × 3) = 2¹ × 3² and (3 × 3 × 3 × 3) = 3⁴ respectively. LCM of 18 and 81 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3⁴ = 162.
Hence, the LCM of 18 and 81 by prime factorization is 162.

LCM of 18 and 81 by Division Method

To calculate the LCM of 18 and 81 by the division method, we will divide the numbers(18, 81) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 81.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 81. Write this prime number(2) on the left of the given numbers(18 and 81), separated as per the ladder arrangement.
Step 2: If any of the given numbers (18, 81) 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 18 and 81 is the product of all prime numbers on the left, i.e. LCM(18, 81) by division method = 2 × 3 × 3 × 3 × 3 = 162.

☛ Also Check:

LCM of 18 and 81 Examples

Example 1: The product of two numbers is 1458. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 1458
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1458/9
Therefore, the LCM is 162.
The probable combination for the given case is LCM(18, 81) = 162.
Example 2: The GCD and LCM of two numbers are 9 and 162 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 = (9 × 162)/18
⇒ z = 81
Therefore, the other number is 81.
Example 3: Verify the relationship between GCF and LCM of 18 and 81.

Solution:

The relation between GCF and LCM of 18 and 81 is given as,
LCM(18, 81) × GCF(18, 81) = Product of 18, 81
Prime factorization of 18 and 81 is given as, 18 = (2 × 3 × 3) = 2¹ × 3² and 81 = (3 × 3 × 3 × 3) = 3⁴
LCM(18, 81) = 162
GCF(18, 81) = 9
LHS = LCM(18, 81) × GCF(18, 81) = 162 × 9 = 1458
RHS = Product of 18, 81 = 18 × 81 = 1458
⇒ LHS = RHS = 1458
Hence, verified.

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FAQs on LCM of 18 and 81

What is the LCM of 18 and 81?

The LCM of 18 and 81 is 162. To find the LCM (least common multiple) of 18 and 81, we need to find the multiples of 18 and 81 (multiples of 18 = 18, 36, 54, 72 . . . . 162; multiples of 81 = 81, 162, 243, 324) and choose the smallest multiple that is exactly divisible by 18 and 81, i.e., 162.

What is the Least Perfect Square Divisible by 18 and 81?

The least number divisible by 18 and 81 = LCM(18, 81)
LCM of 18 and 81 = 2 × 3 × 3 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 18 and 81 = LCM(18, 81) × 2 = 324 [Square root of 324 = √324 = ±18]
Therefore, 324 is the required number.

If the LCM of 81 and 18 is 162, Find its GCF.

LCM(81, 18) × GCF(81, 18) = 81 × 18
Since the LCM of 81 and 18 = 162
⇒ 162 × GCF(81, 18) = 1458
Therefore, the GCF = 1458/162 = 9.

What is the Relation Between GCF and LCM of 18, 81?

The following equation can be used to express the relation between GCF and LCM of 18 and 81, i.e. GCF × LCM = 18 × 81.

Which of the following is the LCM of 18 and 81? 21, 42, 12, 162

The value of LCM of 18, 81 is the smallest common multiple of 18 and 81. The number satisfying the given condition is 162.

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