LCM of 18 and 30 is the smallest number among all common multiples of 18 and 30. The first few multiples of 18 and 30 are (18, 36, 54, 72, . . . ) and (30, 60, 90, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 18 and 30 - by prime factorization, by division method, and by listing multiples.
| 1. | LCM of 18 and 30 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 18 and 30?
Answer: LCM of 18 and 30 is 90.
Explanation:
The LCM of two non-zero integers, x(18) and y(30), is the smallest positive integer m(90) that is divisible by both x(18) and y(30) without any remainder.
Methods to Find LCM of 18 and 30
The methods to find the LCM of 18 and 30 are explained below.
- By Prime Factorization Method
- By Listing Multiples
- By Division Method
LCM of 18 and 30 by Prime Factorization
Prime factorization of 18 and 30 is (2 × 3 × 3) = 21 × 32 and (2 × 3 × 5) = 21 × 31 × 51 respectively. LCM of 18 and 30 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 30 by prime factorization is 90.
LCM of 18 and 30 by Listing Multiples
To calculate the LCM of 18 and 30 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, . . . ) and 30 (30, 60, 90, 120, . . . . )
- Step 2: The common multiples from the multiples of 18 and 30 are 90, 180, . . .
- Step 3: The smallest common multiple of 18 and 30 is 90.
∴ The least common multiple of 18 and 30 = 90.
LCM of 18 and 30 by Division Method
To calculate the LCM of 18 and 30 by the division method, we will divide the numbers(18, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 18 and 30.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 18 and 30. Write this prime number(2) on the left of the given numbers(18 and 30), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (18, 30) 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 30 is the product of all prime numbers on the left, i.e. LCM(18, 30) by division method = 2 × 3 × 3 × 5 = 90.
☛ Also Check:
- LCM of 8 and 28 - 56
- LCM of 18, 36 and 27 - 108
- LCM of 70, 105 and 175 - 1050
- LCM of 42 and 70 - 210
- LCM of 8 and 12 - 24
- LCM of 16 and 28 - 112
- LCM of 21, 28, 36 and 45 - 1260
LCM of 18 and 30 Examples
Example 1: The product of two numbers is 540. If their GCD is 6, what is their LCM?
Solution:
Given: GCD = 6
product of numbers = 540
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 540/6
Therefore, the LCM is 90.
The probable combination for the given case is LCM(18, 30) = 90.Example 2: The GCD and LCM of two numbers are 6 and 90 respectively. If one number is 18, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 18 × y
⇒ y = (GCD × LCM)/18
⇒ y = (6 × 90)/18
⇒ y = 30
Therefore, the other number is 30.Example 3: Find the smallest number that is divisible by 18 and 30 exactly.
Solution:
The smallest number that is divisible by 18 and 30 exactly is their LCM.
⇒ Multiples of 18 and 30:- Multiples of 18 = 18, 36, 54, 72, 90, 108, 126, . . . .
- Multiples of 30 = 30, 60, 90, 120, 150, 180, 210, . . . .
Therefore, the LCM of 18 and 30 is 90.
Show Solution >
go to slidego to slidego to slide
Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.
Book a Free Trial Class
FAQs on LCM of 18 and 30
What is the LCM of 18 and 30?
The LCM of 18 and 30 is 90. To find the least common multiple of 18 and 30, we need to find the multiples of 18 and 30 (multiples of 18 = 18, 36, 54, 72 . . . . 90; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 18 and 30, i.e., 90.
Which of the following is the LCM of 18 and 30? 3, 40, 24, 90
The value of LCM of 18, 30 is the smallest common multiple of 18 and 30. The number satisfying the given condition is 90.
What is the Least Perfect Square Divisible by 18 and 30?
The least number divisible by 18 and 30 = LCM(18, 30)
LCM of 18 and 30 = 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 18 and 30 = LCM(18, 30) × 2 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.
If the LCM of 30 and 18 is 90, Find its GCF.
LCM(30, 18) × GCF(30, 18) = 30 × 18
Since the LCM of 30 and 18 = 90
⇒ 90 × GCF(30, 18) = 540
Therefore, the GCF = 540/90 = 6.
How to Find the LCM of 18 and 30 by Prime Factorization?
To find the LCM of 18 and 30 using prime factorization, we will find the prime factors, (18 = 2 × 3 × 3) and (30 = 2 × 3 × 5). LCM of 18 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 18 and 30.
⇒ LCM of 18, 30 = 21 × 32 × 51 = 90.
