220 LearnersLast updated on May 26th, 2025
LCM of 15 and 30
LCM of two numbers is an integer that can divide both the numbers completely without the remainder. In our daily life, LCM is being used for synchronization of traffic lights or putting the alarm of the clock regularly.
What is the LCM of 15 and 30?
We can simplify the arithmetic operations with fractions by equating the denominators and in other mathematical scenarios by using the LCM. The smallest positive integer, and a multiple of both 15 and 30, is the LCM of the numbers.
How to find the LCM of 15 and 30 ?
LCM is one of the easiest mathematical problems taught in school. There are many methods for calculating LCM of numbers. Here we are listing few of them below -
LCM of 15 and 30 using the Listing multiples method
The LCM of 15 and 30 can be found using the following steps;
Step 1: Write down the multiples of each number:
Multiples of 15 = 15,30,…
Multiples of 30 = 30,60,…
Step 2: Find the smallest multiple from the listed multiples. The LCM of the numbers 15 and 30 is 30.
LCM of 15 and 30 using the Prime Factorization
The highest power of the prime factors is multiplied to get the LCM after the prime factors of each number are written.
Step1: Find the prime factors of the numbers:
Prime factorization of 15 = 5×3
Prime factorization of 30 = 2×5×3
Step2: To find the LCM, multiply the highest power of each factor.
LCM (15,30) = 30
LCM of 15 and 30 using the Division Method
The Division Method involves dividing the numbers by their prime factors and multiplying the divisors in the first column to find the LCM.
Step 1:Write down the numbers 15 and 30 in a row;
Step 2:A prime integer that is evenly divisible into at least one of the numbers out of 15 and 30 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 carry forward 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 (15,30) = 30
Common Mistakes and how to avoid them in LCM of 15 and 30
While calculating LCM of 15 and 30, students make unique mistakes related to it. Few mistakes are as follows -
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 15 and 30, Examples
Problem 1
The LCM of 15 and x is 30. Find x.
LCM(15,x) = 30
Prime factorization of 15 = 5×3
Prime factorization of 30 = 2×5×3
Explanation
The only missing prime factor that 15 doesn't account for is 2. The missing number therefore, must be 2×5×3 = 30. x = 30.
Problem 2
Prove → LCM(a,b)×HCF(a,b)=a×b in the case of 15 and 30.
LCM of 15,30
5×3 becomes the prime factorization of 15
2×5×3 becomes the prime factorization for 30
LCM(15,30) = 30
HCF of 15,30;
Factors of 15 = 1,3,5,15
Factors of 30 = 1,2,3,5,6,10,15,30
HCF(15,30) = 15
Now applying the formula;
LCM(a,b)×HCF(a,b)=a×b
LCM(15,30)×HCF(15,30)=15×30
30×15=15×30
450=450
Explanation
LHS = RHS, the verification is hence justified. The property applied; The product of HCF and LCM of a and b is equal to the product of a and b themselves.
Problem 3
Find the LCM of 15 and 30 using → LCM(a,b)=|a×b|/HCF(a,b)
HCF of 15,30;
Factors of 15 = 1,3,5,15
Factors of 30 = 1,2,3,5,6,10,15,30
HCF(15,30) = 15
Now using the formula;
LCM(a,b)=|a×b|/HCF(a,b)
LCM(15,30)=|15×30|/15
LCM(15,30)=450/15
LCM(15,30)=30
Explanation
Using → LCM(a,b)=|a×b|/HCF(a,b), we find the LCM of the numbers 15 and 30, quickly if you already know the HCF of the numbers.
FAQ’s on LCM of 15 and 30
1.List the multiples of 15 and 30.
2.What is the HCF of 15 and 30?
3.What is the LCM of 10,15 and 30?
4.What is the LCM of 15,24 and 30?
5.What is the LCM of 12,15 and 30?
6.How can children in Qatar use numbers in everyday life to understand LCM of 15 and 30?
7.What are some fun ways kids in Qatar can practice LCM of 15 and 30 with numbers?
8.What role do numbers and LCM of 15 and 30 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 15 and 30 skills?
Important glossaries for LCM of 15 and 30
- Multiple: It is a product of a number and any natural integer. So for 15, both 3 and 5 are the multiples.
- Prime Factor : It is a prime number that one gets after factorization of any given number. Like for 15, both 3 and 5 are prime factors as they can be divided by 1 or the number itself.
- Prime Factorization: It is a process of dividing the number into prime factors.
- Co-prime numbers: These are the positive integers where both the numbers can be divided only by 1. So, both 3 and 5 are co-prime numbers.
- Fraction:It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 3/5–3 is the numerator and 5 is the denominator. Proper fraction is where numerator is always lesser than denominator.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
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