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131 LearnersLast updated on December 30th, 2024
LCM of 40 and 50
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 40 and 50. By learning the following tricks, you can learn the LCM of 40 and 50 easily.
What Is the LCM of 40 and 50?
The LCM of 40 and 50 is 200. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more numbers in different ways.
How to find the LCM of 40 and 50?
We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:
Method 1: Listing of Multiples
Method 2: Prime Factorization
Method 3: Division Method
Now let us delve further into these three methods and how it benefits us.
LCM of 40 and 50 Using Listing of Multiples Method
In this method, we will list all the multiples of 40 and 50. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 40
40, 80, 120, 160, 200, 240, 280,...
Multiples of 50:
50, 100, 150, 200, 250,...
The LCM of 40 and 50 is 200. 200 is the smallest number which can be divisible by both 40 and 50.
LCM of 40 and 50 Using Prime Factorization
To find the LCM of 40 and 50 using the prime factorization method, we need to find out the prime factors of both the numbers. Then multiply the highest powers of the factors to get the LCM.
Prime Factors of 40 are: 23, 51
Prime Factors of 50 are: 21, 52.
Multiply the highest power of both the factors: 23 × 52 = 8 × 5 × 5 = 200
Therefore, the LCM of 40 and 50 is 200.
LCM of 40 and 50 Using Division Method
To calculate the LCM using the division method. We will divide the given numbers with their prime numbers. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the remainder becomes 1. By multiplying the prime factors, one can get LCM.
For finding the LCM of 40 and 50 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 40 and 50.
2 × 2 × 2 × 5 × 5 = 200
The LCM of 40 and 50 is 200
Common Mistakes and How to Avoid Them in LCM of 40 and 50.
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
Mistake 1
Missing a prime factor
Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
LCM of 40 and 50 Examples
Problem 1
Two machines, A and B, are working on a manufacturing line. Machine A completes a batch in 40 minutes, and Machine B completes the similar batch in 50 minutes. In how long will the machines complete a batch?
First, find the LCM of 40 and 50 to determine when both machines will finish a batch at the same time.
Prime factors of 40=23×5 and Prime factors of 50=2×52
Take the highest power:
For 2: 23
For 5: 52
LCM=23×52=8×25=200 minutes
Explanation
The problem asks for the LCM of the two times (40 and 50 minutes) to determine the point at which both machines complete a batch simultaneously.
Problem 2
A factory worker, Sam, can finish assembling a machine part in 40 minutes. His colleague, Mia, can complete the same task in 50 minutes. If they work together, how long will it take them to assemble one part?
Calculate Sam’s and Mia’s work rates (parts per minute):
Sam’s rate=1/40 and Mia’s rate=1/50
The combined rate of Sam and Mia:
1/40+1/50=5+4/200=9/200 parts per minute
Time to complete one part together:
1/(9/200)=200/9≈22.22 minutes
Explanation
We calculate the rate at which each worker completes a part and then add these rates to get the combined rate when they work together. By taking the reciprocal of their combined rate, we determine the total time they need to complete one part together.
Problem 3
A production unit requires components to arrive from two separate suppliers. Supplier A delivers every 40 minutes, and Supplier B delivers every 50 minutes. Using the formula for LCM, calculate the earliest time both suppliers will deliver components at the same time in hours.
Use the formula for LCM, where a and b are two numbers:
LCM (a, b) = a × b / GCF (a, b)
Calculate GCF of 40 and 50:
GCF(40, 50) = 10
Find the LCM:
LCM(40,50)=40×50/10=200 minutes
Convert 200 minutes to hours:
200÷60=3.33 hours
Explanation
Using the LCM formula allows us to calculate the earliest simultaneous delivery time. The LCM finds when two different intervals align, and converting minutes to hours provides a clear answer in the requested time units.
FAQs on the LCM of 40 and 50
1.What is the GCF of 40 and 50?
2.What is the LCM of 30,40 and 50?
3.What is the LCM of 40 and 65?
4. What goes into 40 and 50?
5. Prime factorize 50
Important glossaries for the LCM of 40 and 50
- Prime Number: Any number that has only 2 factors is called a prime number.For 5 and 7, only common factors are 1 and the number itself.
- Composite Number: Any number that has more than 2 factors is called a composite number. For example, 4,8 and 10.
- Prime Factorization: It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number.
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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.
