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136 LearnersLast updated on December 30th, 2024
LCM of 16 and 40
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 16 and 40. By learning the following tricks, you can learn the LCM of 16 and 40 easily.
What Is the LCM of 16 and 40?
The LCM of 16 and 40 is 80. 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 16 and 40?
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 16 and 40 Using Listing of Multiples Method
In this method, we will list all the multiples of 16 and 40. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 16:
16,32,48,64,80,96,112,128,144,160,176,192,…
Multiples of 40:
40,80,120,160,200,240,280,320,360,400,440,480,....
The LCM of 16 and 40 is 80. 80 is the smallest number which can be divisible by both 16 and 40.
LCM of 16 and 40 Using Prime Factorization
To find the LCM of 16 and 40 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 16 are: 24
Prime Factors of 40 are: 23 and 51.
Multiply the highest power of both the factors: 24 × 51 = 2 × 2 × 2 × 2 × 5 = 80
Therefore, the LCM of 16 and 40 is 80.
LCM of 16 and 40 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 16 and 40 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 16 and 40.
2 × 2 × 2 × 2 × 5 = 80
The LCM of 16 and 40 is 80.
Common Mistakes and How to Avoid Them in LCM of 16 and 40.
LCM of 16 and 40 Examples
Problem 1
An athlete completes one lap around a circular track every 16 seconds, and another every 40 seconds. After how many seconds will both athletes be at the starting point again?
Explanation
Problem 2
Given two numbers, 16 and 40, verify that the product of the two numbers is equal to the product of their LCM and GCF.
Explanation
Problem 3
Two workers, X and Y, are hired to complete a task. Worker X completes a cycle of work every 16 minutes, while Worker Y completes a cycle every 40 minutes. If both start working together, how long will it take them to align their cycles?
Explanation
FAQs on the LCM of 16 and 40
1. What is the GCF of 16 and 40?
2.What is the prime factorization of 16 and 40?
3.What is the LCM of 12,16 and 40?
4.What are the factor pairs of 40?
5.Is 40 a factor of 1000?
Important Glossaries for the LCM of 16 and 40
- Prime Number: Any number that has only 2 factors is called a prime number.For example, 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.
