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133 LearnersLast updated on December 2nd, 2024
LCM Of 22 And 33
The Least Common Multiple (LCM) is the smallest number that when we divide by two or more numbers at a time, all three or more numbers divide into it. LCM also helps in math problems and everyday things like event planning or buying supplies. We will find the LCM of 22 and 33 together and what that really means.
What Is The LCM Of 22 And 33?
The LCM or the least common multiple of 2 numbers is the smallest number that appears as a multiple of both numbers. In the case of 22 and 33, The LCM is 66. But how did we get to this answer? There are different ways to obtain a LCM of 2 or more numbers. Let us take a look at those methods.
How To Find The LCM Of 22 And 33
Remember that we previously said there are plenty of ways to calculate the LCM of two numbers or more. Then some of those methods make it extremely easy for us to find the LCM of any two numbers. Those methods are:
- Listing of Multiples
- Prime Factorization
- Division Method
Finally, now we will learn how each of these methods can help us to calculate the LCM of given numbers.
Finding LCM Of 22 And 33 By Listing Of Multiples
This method will help us find the LCM of the numbers by listing the multiples of the given numbers. Let us take a step by step look at this method.
Step 1: The first step is to list all the multiples of the given numbers.
Multiples Of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198 and 220
Multiples Of 33: 33, 66, 99, 132, 165, 198, 231, 264, 297 and 330.
Step 2: The second step is to find the smallest common multiples in both the numbers. In this case, that number is 66 as highlighted above.
By this way, we will be able to tell the LCM of given numbers.
Finding The LCM By Prime Factorization
Let us break down the process of prime factorization into steps and make it easy for children to understand.
The first step is to break down the given numbers into its primal form. The primal form of the number is:
22= 11×2
33= 11×3
As you can see, 11 appears as a prime factor in both numbers. So instead of considering 11 two times, we will only consider it once. So the final equation will look like (11×3×2).
So after the multiplication, we will be getting the LCM as 66.
As you can see, using this method can be easier for larger numbers compared to the previous method.
Finding The LCM By Division Method
The method to calculate the LCM is really simple. We’ll break these given numbers apart till it comes down to one, by dividing it by the prime factors. The product of the divisors that will come is the LCM of the given numbers.
Let us understand it step by step:
The first thing is to find the number common in both the numbers. Here it is 11. In that case, we divide both the numbers by 11. It will reduce the values of the numbers to 2 and 3.
2 and 3 are a prime number, it can be divided by only 2 and 3. That means after dividing, there will be only 1’s in the last row.
This is the end of the division. However, we will now find the product of the numbers on the left. The numbers on the left side are 2, 3, and 11.
These numbers multiplied give 66. On this basis, therefore, the LCM of the 22 and 33 becomes 66.
Common Mistakes That Are Made And How To Avoid Them For LCM Of 22 And 33.
LCM Of 22 And 33 Examples
Problem 1
If two events repeat every 22 and 33 days, when do they overlap first?
Explanation
Problem 2
Emma jogs every 22 days and Leo every 33 days. How many days until they jog together?
Explanation
Problem 3
Two trains pass by every 22 and 33 minutes. How long until they pass together again?
Explanation
Problem 4
Two water fountains turn on every 22 and 33 seconds. When will they turn on at the same time?
Explanation
Problem 5
In how many days do 22- and 33-day events first match?
Explanation
FAQs For LCM Of 22 And 33
1.What’s the GCF of 22 and 33, and how does it relate to LCM?
2.What is the prime factorization of 12 and 24?
3.Can the LCM of 2 and 3 be found by listing multiples?
4.How can we quickly determine whether 66 is the LCM of 22 and 33?
Important Glossaries for LCM of 22 qnd 33
- Least Common Multiple (LCM): The smallest number that can be evenly divided by two or more numbers without any leftovers.
- Multiple: A number that can be obtained by multiplying a given number by an integer (e.g., multiples of 2 are 2, 4, 6, 8, etc.).
- Prime Factorization: Breaking down a number into its prime factors. For example, the prime factorization of 22 is 2 × 11.
- Divisor: A number that divides another number evenly. For example, 3 is a divisor of 12 because 12 ÷ 3 = 4.
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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.
