194 LearnersLast updated on May 26th, 2025
LCM of 18 and 30
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 18 and 30. In this article, we will learn more about the LCM and how to find the LCM of 18 and 30 using different methods.
What is the LCM of 18 and 30?
The LCM of 18 and 30 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.
How to find the LCM of 18 and 30 ?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 18 and 30 using the Listing multiples method
The LCM of 18 and 30 can be found using the following steps;
Step 1:Write down the multiples of each number:
Multiples of 18 = 18,36,54,72,90,…
Multiples of 30 = 30,60,90,…
Step 2: Ascertain the smallest multiple from the listed multiples of 18 and 30. The least common multiple of the numbers 18 and 30 is 90.
LCM of 18 and 30 using the Prime Factorization
The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.
Step 1: Find the prime factors of the numbers:
Prime factorization of 18 = 3×3×2
Prime factorization of 30 = 2×5×3
Step 2: Multiply the highest power of each factor ascertained to get the LCM:
LCM (18,30) = 90
LCM of 18 and 30 using the Division Method
The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM.
Step 1:Write down the numbers in a row;
Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers.
Step 3: Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.
Step 4: The LCM of the numbers is the product of the prime numbers in the first column, i.e,
LCM (18,30) = 90
Common Mistakes and how to avoid them while finding the LCM of 18 and 30
Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 18 and 30, make a note while practicing.
Mistake 1
Stopping at ‘a’ common multiple
Students often overlook the least common multiple and assume that a common multiple is the LCM of the given digits. Emphasis lies on the word ‘least’ while trying to find the LCM.
LCM of 18 and 30, Examples
Problem 1
LCM of a and b is 90. a=18, find b.
LCM(18,b) = 90
We apply the below formula to find the missing number;
LCM(a,b)×HCF(a,b)=a×b
With the given figures, we rearrange the formula as;
90×HCF(18,b) = 18×b
Explanation
b must have the prime factors 2,3 and 5, for the LCM of 18 and b to be equal to 90.
The number with the mentioned as its factors is 30.
Verifying LCM(18,30) = 90
Therefore, we can conclude that the missing number is 30.
Problem 2
Verify the relationship between the LCM and HCF of 18 and 30.
We apply the formula → LCM(a,b)×HCF(a,b)=a×b to check the relationship between thew numbers;
LCM of 18 and 30;
Prime factorization of 18 = 3×3×2
Prime factorization of 30 = 2×5×3
LCM (18,30) = 90
HCF of 18 and 30;
Factors of 18 = 1,2,3,6,9,18
Factors of 30 = 1,2,3,5,6,10,15,30
HCF(18,30) = 6
Now, verifying the same;
LCM(a,b)×HCF(a,b)=a×b
90×6=18×30
540=540
Explanation
The above is how we ascertain and verify the relationship between the LCM and the HCF of two given numbers. It is based on the principle that the product of the HCF and the LCM is equal to the product of the numbers a and b themselves.
Problem 3
The LCM of a and b is 90. a=18, what could be the smallest value of b? The HCF of the numbers a and b is a divisor of 6.
LCM(18,b) = 90
HCF (18,b) → a divisor of 6
Possible values of the HCF could be → 1,2,3,6 (factors of 6)
Now we try the factors to fit the condition;
When HCF = 1,
LCM(a,b)×HCF(a,b)=a×b
LCM(18,b)×HCF(18,b)=18×b
90×1 =18×b → b = 90/18 = 5
LCM (18,5) = 90, but 5 is not a divisor of 6, this case is invalid.
When HCF= 6,
LCM(a,b)×HCF(a,b)=a×b
LCM(18,b)×HCF(18,b)=18×b
90×6 =18×b → b = 30
Explanation
b=30, satisfies both the conditions, i.e., the LCM = 90, 30 is a divisor of 6.
Problem 4
FAQs on the LCM of 18 and 30
What is the HCF of 28 and 30 ?
Explanation
Factors of 28 = 1,2,4,7,14,28
Factors of 30 = 1,2,3,5,6,10,15,30
HCF (28,30) = 2
Problem 5
What is the ratio between the HCF and LCM of 18 and 30?
HCF(18,30) = 6
LCM (8,30) = 90
Ratio = 90/6=15
Explanation
What is the LCM of 18,24 and 30?
Important glossaries for LCM of 18 and 30
- Multiple: A number and any integer multiplied.
- Prime Factor: A natural number (other than 1) that has factors that are one and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.
- Relatively Prime Numbers: Numbers that have no common factors other than 1.
- Fraction: A representation of a part of a whole.
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