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143 LearnersLast updated on December 24th, 2024
LCM OF 8,10 AND 12
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 8, 10, and 12. By learning the following tricks, you can learn the LCM of 8, 10, and 12 easily.
What is the LCM of 8,10 and12?
The LCM of 8, 10, and 12 is 120. 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 8,10 and 12?
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 8, 10, and 12 Using Listing the Multiples
In this method, we will list all the multiples of 8, 10, and 12. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 8: 8,16,24,32,40,48,56,64,72,80,88,96.104,112,120
Multiples of 10:10,20,30,40,50,60,70,80,90,100,11,120
Multiples of 12:12,24,36,48,60,72,84,96,108,120
The LCM of 8, 10, and 12 is 120. 120 is the smallest number which can be divisible by both 8, 10, and 12.
LCM of 8, 10, and 12 Using Prime Factorization
To find the LCM of 8, 10, and 12 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 8: 23
Prime Factors of 10: 21 × 51
Prime Factors of 12: 22 × 31
Multiply the highest power of both the factors: 23 x 31 x 51 = 120
Therefore, the LCM of 8, 10, and 12 is 120.
LCM Of 8,10, and 12 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 8, 10, and 12 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 8, 10, and 12.
2 × 2 × 2 × 3 × 5 = 120
The LCM of 8, 10, and 12 is 120.
Common Mistakes and How to Avoid Them in LCM of 8,10 and 12
LCM OF 8,10 and 12 Examples
Problem 1
Find the smallest number that is divisible by 8,10,12 exactly.
Explanation
Problem 2
Finding the GCF of 8,10 and 12?
Explanation
Problem 3
Machine A beeps every 8 minutes, machine B beeps every 10 minutes, machine C every 12 minutes. When will they next beep together?
Explanation
Problem 4
A bus travels to the mall every 8 hours, another bus travels to the mall every 10 hours. A third bus travels to the same mall every 12 hours. How many hours will it take for all three buses to meet at the same time?
Explanation
Problem 5
Andy has swimming class every 8 days, drawing class every 10 days, and math class every 12 days. On which day would all three classes happen on the same day?
Explanation
FAQs on Least Common Multiple of 8,10, and 12
1.What is the full form of LCM?
2.What is the GCF of 8,10 and 12?
3.What is the LCM of 8,10,12?
4.What is the LCM of 8,9, and 12?
5.What is the LCM of 24,8, and 12?
Important Glossaries on the LCM of 8,10 and 12
- 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.
