166 LearnersLast updated on May 26th, 2025
LCM of 30 and 45
The Least common multiple (LCM) is the smallest number that is divisible by the numbers 30 and 45. The LCM can be found using the listing multiples method, the prime factorization, and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycles of events.
How to Find the LCM of 30 and 45?
There are various methods to find the LCM, Listing method, prime factorization method, and division method are explained below;
LCM of 30 and 45 using the Listing Multiples Method
The LCM of 30 and 45 can be calculated using the following steps:
Step 1:Write down the multiples of each number
— Multiples of 30 = 30, 60, 90,…
— Multiples of 45 = 45, 90, 135,…
Step 2:Ascertain the smallest multiple from the listed multiples:
— The smallest common multiple is 90.
Thus, LCM(30,45) = 90
LCM of 30 and 45 using the Prime Factorization Method
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 each number:
— Prime factorization of 30 = 21×31×51
— Prime factorization of 45 = 32×51
Step 2: Take the highest powers of each prime factor and multiply the highest powers to get the LCM:
LCM(30,45) = 90
LCM of 30 and 45 using the Division Method
This method involves dividing both numbers by their common prime factors and multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors, and multiply the divisors.
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. 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 3:The LCM of the numbers is the product of the prime numbers in the first column, i.e,
2×3×3×5 =90
Thus, LCM(32,48)=90
Common Mistakes and how to avoid them while finding the LCM of 30 and 45
Students might make mistakes while finding the Least common multiples. By understanding the common errors, they can perform better calculations.
Mistake 1
Misunderstanding the LCM from GCD, and calculate incorrectly.
Teach the student to be aware of the differentiation between LCM and GCD, to extract accurate answers of LCM.
FAQs for the LCM of 30 and 45
1.What is the HCF of 45 and 30?
2.What is the LCM of 30 and 40?
3.What is the LCM of 30 and 44?
4.What is the LCM of 30 and 60?
5.What is the LCM of 27 and 45?
6.How can children in Vietnam use numbers in everyday life to understand LCM of 30 and 45?
7.What are some fun ways kids in Vietnam can practice LCM of 30 and 45 with numbers?
8.What role do numbers and LCM of 30 and 45 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve LCM of 30 and 45 skills?
Important glossaries for the LCM of 32 and 48
- 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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About BrightChamps in Vietnam
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
: She loves to read number jokes and games.
