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LCM of 18 and 45

LCM of 18 and 45 is the smallest number among all common multiples of 18 and 45. The first few multiples of 18 and 45 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (45, 90, 135, 180, 225, 270, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 45 - by listing multiples, by prime factorization, and by division method.

1.	LCM of 18 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 18 and 45?

Answer: LCM of 18 and 45 is 90.

Explanation:

The LCM of two non-zero integers, x(18) and y(45), is the smallest positive integer m(90) that is divisible by both x(18) and y(45) without any remainder.

Methods to Find LCM of 18 and 45

Let's look at the different methods for finding the LCM of 18 and 45.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 18 and 45 by Division Method

To calculate the LCM of 18 and 45 by the division method, we will divide the numbers(18, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 45.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 45. Write this prime number(2) on the left of the given numbers(18 and 45), separated as per the ladder arrangement.
Step 2: If any of the given numbers (18, 45) 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 45 is the product of all prime numbers on the left, i.e. LCM(18, 45) by division method = 2 × 3 × 3 × 5 = 90.

LCM of 18 and 45 by Prime Factorization

Prime factorization of 18 and 45 is (2 × 3 × 3) = 2¹ × 3² and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 18 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ = 90.
Hence, the LCM of 18 and 45 by prime factorization is 90.

LCM of 18 and 45 by Listing Multiples

To calculate the LCM of 18 and 45 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, 108, 126, . . . ) and 45 (45, 90, 135, 180, 225, 270, . . . . )
Step 2: The common multiples from the multiples of 18 and 45 are 90, 180, . . .
Step 3: The smallest common multiple of 18 and 45 is 90.

∴ The least common multiple of 18 and 45 = 90.

☛ Also Check:

LCM of 18 and 45 Examples

Example 1: The product of two numbers is 810. If their GCD is 9, what is their LCM?

Solution:

Given: GCD = 9
product of numbers = 810
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 810/9
Therefore, the LCM is 90.
The probable combination for the given case is LCM(18, 45) = 90.
Example 2: Verify the relationship between GCF and LCM of 18 and 45.

Solution:

The relation between GCF and LCM of 18 and 45 is given as,
LCM(18, 45) × GCF(18, 45) = Product of 18, 45
Prime factorization of 18 and 45 is given as, 18 = (2 × 3 × 3) = 2¹ × 3² and 45 = (3 × 3 × 5) = 3² × 5¹
LCM(18, 45) = 90
GCF(18, 45) = 9
LHS = LCM(18, 45) × GCF(18, 45) = 90 × 9 = 810
RHS = Product of 18, 45 = 18 × 45 = 810
⇒ LHS = RHS = 810
Hence, verified.
Example 3: The GCD and LCM of two numbers are 9 and 90 respectively. If one number is 18, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 18 × m
⇒ m = (GCD × LCM)/18
⇒ m = (9 × 90)/18
⇒ m = 45
Therefore, the other number is 45.

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FAQs on LCM of 18 and 45

What is the LCM of 18 and 45?

The LCM of 18 and 45 is 90. To find the least common multiple (LCM) of 18 and 45, we need to find the multiples of 18 and 45 (multiples of 18 = 18, 36, 54, 72 . . . . 90; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 18 and 45, i.e., 90.

What is the Relation Between GCF and LCM of 18, 45?

The following equation can be used to express the relation between GCF and LCM of 18 and 45, i.e. GCF × LCM = 18 × 45.

How to Find the LCM of 18 and 45 by Prime Factorization?

To find the LCM of 18 and 45 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (45 = 3 × 3 × 5). LCM of 18 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 45.
⇒ LCM of 18, 45 = 2¹ × 3² × 5¹ = 90.

What is the Least Perfect Square Divisible by 18 and 45?

The least number divisible by 18 and 45 = LCM(18, 45)
LCM of 18 and 45 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 18 and 45 = LCM(18, 45) × 2 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

If the LCM of 45 and 18 is 90, Find its GCF.

LCM(45, 18) × GCF(45, 18) = 45 × 18
Since the LCM of 45 and 18 = 90
⇒ 90 × GCF(45, 18) = 810
Therefore, the GCF (greatest common factor) = 810/90 = 9.

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