183 LearnersLast updated on May 26th, 2025
LCM of 30 and 50
The LCM or Least Common Multiple of numbers is the smallest number which can be exactly divisible by each of the numbers. It can also be defined as the least common number, which is a common multiple of the numbers given. LCM helps in scheduling and coordinating prices, events, also used for revising timetables, etc.
How to find the LCM of 30 and 50
To find the LCM of 30 and 50 we will learn some methods:
- Listing Method
- Prime Factorization Method
- Division Method
LCM of 30 and 50 Using Listing the Multiples
The Listing Multiples method is one of the methods used to find LCM of some given numbers. We have to know the multiples of the given numbers and then apply this method.
Step 1: List down the multiples of each number
Multiples of 30 = 30,60,90,120,150,180,210,240,270,300,...
Multiples of 50= 50,100,150,200,250,300,350,400,450,500,...
Step 2: Find out the smallest multiple from the listed multiples
The smallest common multiple is 150
Thus, LCM (30,50) = 150.
LCM of 30 and 50 Using Prime Factorization
Rule: The prime factorization of each number is to be done, and then the highest power of the prime factors are multiplied to get the LCM.
Step 1: Find the prime factorization of the numbers:
Prime factorization of 30 = 3×2×5
Prime factorization of 50 = 52×2
Step 2: Take the highest powers of each prime factor, and multiply the highest powers to
get the LCM
52×2×3 = 150
LCM (30,50) = 150.
LCM of 30 and 50 Using Division Method
This is the most used method to find any LCM. It involves dividing both numbers 30 and 50 by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.
Step 1: Write the numbers, divide by common prime factors. A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers
The first common prime divisors for both 30 and 50 are 2 or 5. We choose 5.
Step 2: Dividing 30 and 50 with 5, we get 6 and 10 respectively.
Step 3: Repeat Step 1 and 2 till both are getting perfectly divided. 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.
5×2×3×5 = 150
Thus, LCM (30,50) = 150
Common Mistakes and How to Avoid Them in LCM of 30 and 50
Misconception is normal, but we should avoid it whenever we are solving math problems. Let us see how we can avoid some common errors.
Mistake 1
Students might make mathematical errors while prime factoring.
Prime factorization is the most important and most basic whenever we try to find LCM. So, Prime Factorization should be done correctly.
LCM of 30 and 50 Examples
Problem 1
The LCM of 30 and 50 is 150. Then what will be the LCM of 40 and 50?
Prime Factorization of 40 =23×5
Prime factorization of 50 = 52×2
LCM(40,50)= 23×52 =200
Explanation
Solved the LCM of 40 and 50 through Prime Factorization method.
Problem 2
LCM (30,50) = x. Find the smallest positive integer (n), where n×x=300 and the smallest positive integer (m), m× x=450
LCM (30,50) = x
We know that the LCM of 30 and 50 from the previous calculations.
LCM (30,50) = 150
n×150=300
⇒ n=300 /150
⇒ n = 2
Similarly,
LCM (30,50) = 150
n×150=450
⇒ n=450 /150
⇒ n = 3
Answer: 2, 3.
Explanation
We made use of the LCM of 30 and 50 and solved the equation to get the value of n in both the problems.
Problem 3
What is the LCM of 30, 50 and 60?
Prime factorization of 30 = 3×2×5
Prime factorization of 50 = 52×2
Prime Factorization of 60 =22×3×5
LCM (30,50,60)= 22×3×52 =300
Answer: 300
Explanation
The LCM of numbers 30,50 and 60 are found using the Prime factorization method.
FAQs on LCM of 30 and 50
1.What is the GCF of 30 and 50?
2.What is the LCM of 25,30, and 50?
3.What is the LCM of 30 and 53?
4.What is the LCM of 30 and 60?
5.What is the LCM of 35 and 50?
6.How can children in Qatar use numbers in everyday life to understand LCM of 30 and 50?
7.What are some fun ways kids in Qatar can practice LCM of 30 and 50 with numbers?
8.What role do numbers and LCM of 30 and 50 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 30 and 50 skills?
Important glossaries for the LCM of 35 and 50
- Prime Factor: A natural number or whole number which has factors that are 1 and itself.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.
- Co-prime numbers: numbers which have the only positive divisor of them both as 1.
- HCF or GCF: GCF (Greatest common factor) is the largest factor that divides both numbers.
- Multiples: The product we get when all the integers are multiplied with a particular number, one by one.
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About BrightChamps in Qatar
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.
