137 LearnersLast updated on May 26th, 2025
LCM OF 12 AND 32
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 12 and 32. By learning the following tricks, you can learn the LCM of 12 and 32 easily.
What is the LCM of 12 and 32?
The LCM of 12 and 32 is 96. 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 32?
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 32 Using Listing the Multiples
In this method, we will list all the multiples of 12 and 32. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 12: 12,24,36,48,60,72,84,96
Multiples of 32:32,64,96,128,160,192…
The LCM of 12 and 32 is 96. 96 is the smallest number which can be divisible by both 12 and 32.
LCM of 12 and 32 Using Prime Factorization
To find the LCM of 12 and 32 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 32 are: 2×2×2×2×2
Multiply the highest power of both the factors: 25 x 31 = 96.
Therefore, the LCM of 12 and 32 is 96.
LCM OF 12 and 32 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 32 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 12 and 32.
2 x 2 x 2 x 2 x 2 x 3 = 96
The LCM of 12 and 32 is 96.
Common Mistakes and How to Avoid Them in LCM of 12 and 32
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
Mistake 1
Confused LCM with GCF
Many of us will get confused between LCM and GCF. LCM is the smallest number which divides both numbers evenly, and GCF is the largest number which divides both numbers evenly.
LCM OF 12 and 32 Examples
Problem 1
What is the LCM of 12 and 32?
The LCM of 12 and 32 is 96
Explanation
The LCM of 12 and 32, is the smallest common number 96 that is divisible by both 32 and 12 without any remainder.
Problem 2
The GCD and LCM of two numbers are 4 and 96 respectively. If one number is 32, find the other number.
Let the other number to be X
therefore, GCD x LCM = 32 × X
X = (GCD x LCM )/32
X = (4 ×96) /32
X = 12
Therefore, the other number is 12
Explanation
The GCD 4 means that 32 and the unknown number (x) have no common factor other than 1. The LCM to 4 and 96 specify that 12 is the smallest number, and it can be divisible by both 32 x. So the product of the number12 and32 is 96
Problem 3
Two machines in a factory run on different cycles, one machine finishes a cycle every 12 minutes, and the other finishes a cycle every 32 minutes. After how many minutes will both machines finish a cycle at the same time?
here, we need to find when the two cycles, that is (12 minutes and 32 minutes)align. So the LCM of 12 and 32 is 96
LCM = 96
Explanation
we find the LCM of 12 and 32 is 96. So that means the two machines will run simultaneously every 96 minutes.
Problem 4
A body builder does one type of workout every 12 days and another type of workout every 32 days. If he performs both the workouts on the same day. After how many days will he perform the same workout on the same day again?
The first workout is done every: 12 days
The second workout is done every: 32 days
So the body builder will perform both workouts on the same day after: Using prime factorization: 25 x 3 = 96 days
Explanation
Using prime factorization: 25 x 3 = 96 days
Problem 5
Erin waters two sets of plants. One set every 12 days and the second set every 32 days. When will she water both plant sets together?
LCM of 12 and 32 = 96
Explanation
Therefore, Erin will water both plant sets on the same day every 96 days.
FAQs on Least Common Multiple of 12 and 32
1.What is the GCF of 32 and 12?
2.What is the LCM of 12 and 32?
3.What are the multiples of 32?
4.What is the LCM of 16, 12 and 32?
5.What is the LCM of 12?
6.How can children in Qatar use numbers in everyday life to understand LCM OF 12 AND 32?
7.What are some fun ways kids in Qatar can practice LCM OF 12 AND 32 with numbers?
8.What role do numbers and LCM OF 12 AND 32 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM OF 12 AND 32 skills?
Important Glossaries for LCM of 12 and 32
- 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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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.
