159 LearnersLast updated on May 26th, 2025
LCM of 36 and 45
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 36 and 45. By learning the following tricks, you can learn the LCM of 36 and 45 easily.
What Is the LCM of 36 and 45?
The LCM of 36 and 45 is 180. 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 36 and 45?
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 36 and 45 Using Listing of Multiples Method
In this method, we will list all the multiples of 36 and 45. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 36:
36, 72, 108, 144, 180, 216, 252, 288, 324, 360,…
Multiples of 45:
45, 90, 135, 180, 225, 270, 315, 360, 405, 450,…
The LCM of 36 and 45 is 180. 180 is the smallest number which can be divisible by both 36 and 45.
LCM of 36 and 45 Using Prime Factorization
To find the LCM of 36 and 45 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 36 are: 22, 32
Prime Factors of 45 are: 32, 51
Multiply the highest power of both the factors: 22 × 32 × 51 = 2 × 2 × 3 × 3 × 5 = 180
Therefore, the LCM of 36 and 45 is 180.
LCM of 36 and 45 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 36 and 45 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 36 and 45
2 × 2 × 3 × 3 × 5 = 180
The LCM of 36 and 45 is 180.
Common Mistakes and How to Avoid Them in LCM of 36 and 45.
Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes.
Mistake 1
Missing a prime factor
Children sometimes may forget to write all the prime factors for a given number. So, at the start we have to write all the prime factors for the given numbers which won’t cause any problems later on.
LCM of 36 and 45 Examples
Problem 1
Find the missing number that would satisfy both conditions for the sequence of common multiples of 36 and 45 up to 540.Given sequence: 0, 180, 360, ?, 720.
LCM (36, 45) = 180
The sequence of multiples: 0, 180, 360
Missing number = 360+180=540
Explanation
The missing figure can be found by adding LCM repeatedly. Here, 180 is added successively to complete the sequence up to the required range.
Problem 2
A person buys 36 pencils and 45 pens. If they wish to distribute both items in equal groups without remainder, what is the maximum number of groups they can make?
Find the GCF of 36 and 45:
GCF=9
Divide the items into groups of 9 each:
Pencils: 36÷9= 4 groups.
Pens: 45÷9=5 groups.
Explanation
The GCF helps determine the largest number of groups possible for a shared divisor between items, showing how GCF and divisibility link in distribution.
Problem 3
If a=36 and b=45, prove that the relationship LCM(a, b)×GCF(a, b)=a×b holds true.
Find the GCF of 36 and 45:
36 = 22 × 32
45 = 32 × 5
GCF = 32 = 9
Find the LCM:
LCM = 180
Verify the relationship:
LCM (36, 45) × GCF (36, 45) = 180 × 9 = 1620
a × b = 36 × 45 = 1620
Therefore, LCM × GCF = Product of the numbers
Thus, the relationship holds true.
Explanation
This example confirms that the product of LCM and GCF for any two numbers is equal to the product of the numbers themselves. Here, it’s verified with 36 and 45.
FAQs on the LCM of 36 and 45
1.What is the prime factorization of 36 and 45?
2.What is the GCF of 36 and 45?
3. What numbers go into 36 and 45?
4.What is the number divisible by 36 and 45?
5.What is the prime factorization of the LCM of 36 and 45?
6.How can children in Saudi Arabia use numbers in everyday life to understand LCM of 36 and 45?
7.What are some fun ways kids in Saudi Arabia can practice LCM of 36 and 45 with numbers?
8.What role do numbers and LCM of 36 and 45 play in helping children in Saudi Arabia develop problem-solving skills?
9.How can families in Saudi Arabia create number-rich environments to improve LCM of 36 and 45 skills?
Important Glossaries for the LCM of 36 and 45
- 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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About BrightChamps in Saudi Arabia
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.
