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165 LearnersLast updated on November 29th, 2024
LCM of 30 and 40
LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events. In this article, we will learn how to learn LCM by using different methods, learn to solve a few problems applying the LCM.
What is the LCM of 30 and 40?
The LCM of 30 and 40 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 30 and 40?
There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;
LCM of 30 and 40 using the Listing multiples method
The LCM of 30 and 40 can be found using the following steps;
Step 1: Write down the multiples of each number:
Multiples of 30–30,60,90,120,150,…
Multiples of 40–40,80,120,…
Step 2: Ascertain the smallest multiple from the listed multiples of 30 and 40.
The LCM of 30 and 40 = 120
LCM of 30 and 40 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 30= 3×5×2
Prime factorization of 40 = 2×2×5×2
Step 2: Multiply the highest power of each factor ascertained to get the LCM:
LCM (30,40) = 120
LCM of 30 and 40 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. 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, LCM (30,40) = 120
Common Mistakes and how to avoid them while finding the LCM of 30 and 40
LCM of 30 and 40, Examples
Problem 1
Verify LCM(a,b)×HCF(a,b)=a×b, where a= 30 and b=40.
Explanation
Problem 2
Find the LCM of 30 and 40 using the formula.
Explanation
Problem 3
Find x where, LCM (30,x)=120 and HCF(30,x)=10.
Explanation
FAQ’s on LCM of 30 and 40
1.What is the HCF of 30 and 40?
2.What are the factors of 30 and 40?
3. What is the LCM of 20,30 and 40?
4. What is the LCM of 32 and 48?
5.What is the HCF of 27 and 90?
Important Glossaries for LCM of 30 and 40
- 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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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.
