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LCM of 18 and 20

LCM of 18 and 20 is the smallest number among all common multiples of 18 and 20. The first few multiples of 18 and 20 are (18, 36, 54, 72, 90, 108, 126, . . . ) and (20, 40, 60, 80, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 20 - by prime factorization, by division method, and by listing multiples.

1.	LCM of 18 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 18 and 20?

Answer: LCM of 18 and 20 is 180.

Explanation:

The LCM of two non-zero integers, x(18) and y(20), is the smallest positive integer m(180) that is divisible by both x(18) and y(20) without any remainder.

Methods to Find LCM of 18 and 20

The methods to find the LCM of 18 and 20 are explained below.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 18 and 20 by Prime Factorization

Prime factorization of 18 and 20 is (2 × 3 × 3) = 2¹ × 3² and (2 × 2 × 5) = 2² × 5¹ respectively. LCM of 18 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ = 180.
Hence, the LCM of 18 and 20 by prime factorization is 180.

LCM of 18 and 20 by Listing Multiples

To calculate the LCM of 18 and 20 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 20 (20, 40, 60, 80, . . . . )
Step 2: The common multiples from the multiples of 18 and 20 are 180, 360, . . .
Step 3: The smallest common multiple of 18 and 20 is 180.

∴ The least common multiple of 18 and 20 = 180.

LCM of 18 and 20 by Division Method

To calculate the LCM of 18 and 20 by the division method, we will divide the numbers(18, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 20.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 20. Write this prime number(2) on the left of the given numbers(18 and 20), separated as per the ladder arrangement.
Step 2: If any of the given numbers (18, 20) 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 20 is the product of all prime numbers on the left, i.e. LCM(18, 20) by division method = 2 × 2 × 3 × 3 × 5 = 180.

☛ Also Check:

LCM of 18 and 20 Examples

Example 1: The product of two numbers is 360. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2
product of numbers = 360
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 360/2
Therefore, the LCM is 180.
The probable combination for the given case is LCM(18, 20) = 180.
Example 2: The GCD and LCM of two numbers are 2 and 180 respectively. If one number is 18, find the other number.

Solution:

Let the other number be b.
∵ GCD × LCM = 18 × b
⇒ b = (GCD × LCM)/18
⇒ b = (2 × 180)/18
⇒ b = 20
Therefore, the other number is 20.
Example 3: Verify the relationship between GCF and LCM of 18 and 20.

Solution:

The relation between GCF and LCM of 18 and 20 is given as,
LCM(18, 20) × GCF(18, 20) = Product of 18, 20
Prime factorization of 18 and 20 is given as, 18 = (2 × 3 × 3) = 2¹ × 3² and 20 = (2 × 2 × 5) = 2² × 5¹
LCM(18, 20) = 180
GCF(18, 20) = 2
LHS = LCM(18, 20) × GCF(18, 20) = 180 × 2 = 360
RHS = Product of 18, 20 = 18 × 20 = 360
⇒ LHS = RHS = 360
Hence, verified.

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FAQs on LCM of 18 and 20

What is the LCM of 18 and 20?

The LCM of 18 and 20 is 180. To find the LCM of 18 and 20, we need to find the multiples of 18 and 20 (multiples of 18 = 18, 36, 54, 72 . . . . 180; multiples of 20 = 20, 40, 60, 80 . . . . 180) and choose the smallest multiple that is exactly divisible by 18 and 20, i.e., 180.

Which of the following is the LCM of 18 and 20? 180, 15, 36, 35

The value of LCM of 18, 20 is the smallest common multiple of 18 and 20. The number satisfying the given condition is 180.

What is the Least Perfect Square Divisible by 18 and 20?

The least number divisible by 18 and 20 = LCM(18, 20)
LCM of 18 and 20 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 18 and 20 = LCM(18, 20) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

What are the Methods to Find LCM of 18 and 20?

The commonly used methods to find the LCM of 18 and 20 are:

Listing Multiples
Prime Factorization Method
Division Method

If the LCM of 20 and 18 is 180, Find its GCF.

LCM(20, 18) × GCF(20, 18) = 20 × 18
Since the LCM of 20 and 18 = 180
⇒ 180 × GCF(20, 18) = 360
Therefore, the GCF (greatest common factor) = 360/180 = 2.

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