Table Of Contents
144 LearnersLast updated on December 24th, 2024
LCM OF 12 and 42
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 12 and 42. By learning the following tricks, you can learn the LCM of 12 and 42 easily.
What is the LCM of 12 and 42
The LCM of 12 and 42 is 84. 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 12 and 42?
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`12 and 42 Using Listing the Multiples
In this method, we will list all the multiples of 12 and 42. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 12: 12,24,36,48,60,72,84…
Multiples of 42: 42,84,126,168,210,252…
The LCM of 12 and 42 is 100. 100 is the smallest number which can be divisible by both 12 and 42.
LCM of 12 and 42 Using Prime Factorization
To find the LCM of 12 and 42 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 12 are: 2×2×3
Prime factors of 42 are: 2×3×7
Multiply the highest power of both the factors: 22 x 31 x 71 = 84
Therefore, the LCM of 12 and 42 is 84
LCM Of 12 and 42 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 12 and 42 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 12 and 42.
2 x 2 x 3 x 7 = 84
The LCM of 12 and 42 is 84
Common Mistakes and How to Avoid Them in LCM of 12 and 42
LCM OF 12 and 42 Examples
Problem 1
Find the smallest number that is divisible by 12,42 exactly.
Explanation
Problem 2
What is the GFC of 12 and 42?
Explanation
Problem 3
Machine A beeps every 12 minutes, and machine B beeps every 42 minutes. When will they next beep together?
Explanation
Problem 4
Two trains cross the same station at different intervals. The first train crosses every 12 minutes, and the second train crosses every 42 minutes. If both trains cross the same station at the same time, when will they cross the station together again?
Explanation
Problem 5
A bus passes a junction every 12 minutes another bus passes the same junction every 42 minutes. If they pass the junction at the same time, how long will it take for both buses to pass the junction at the same time again.
Explanation
FAQs on LCM of 12 and 42
1. Write the LCM of 12 and 42.?
2.What are the GCF and LCM of 12 and 42?
3.What is the LCM of 42?
4.What is the LCM of 12?
5.How to find a GCF of 42?
Important Glossaries for LCM of 12 and 42
- 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.
Explore More numbers
Previous to LCM OF 12 and 42
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.
