144 LearnersLast updated on May 26th, 2025
LCM of 18 and 36
Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 18 and 36. By learning the following tricks, you can learn the LCM of 18 and 36 easily.
What Is the LCM of 18 and 36?
The LCM of 18 and 36 is 36. 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 18 and 36?
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 18 and 36 Using Listing of Multiples Method
In this method, we will list all the multiples of 18 and 36. Then we will try to find a multiple that is present in both numbers.
For example,
Multiples of 18:
18, 36, 54, 72, 90,....
Multiples of 36:
36, 72, 108, 144, 180, ….
The LCM of 18 and 36 is 36. 36 is the smallest number which can be divisible by both 18 and 36.
LCM of 18 and 36 Using Prime Factorization
To find the LCM of 18 and 36 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 18 are: 21, 32.
Prime Factors of 36 are: 22, 32.
Multiply the highest power of both the factors: 22 × 32 = 4 × 9 = 36
Therefore, the LCM of 18 and 36 is 36.
LCM of 18 and 36 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 18 and 36 we will use the following method.
By multiplying the prime divisors from the table, we will get the LCM of 18 and 36.
2 × 2 × 3 × 3 = 36
The LCM of 18 and 36 is 36.
Common Mistakes and How to Avoid Them in LCM of 18 and 36.
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 18 and 36 Examples
Problem 1
Workers A and B can complete a task in 18 hours and 36 hours respectively. If A and B work together, how long will it take?
Calculate the work rate of each worker:
A’s rate = 1/18 of the work per hour.
B’s rate = 1/36​ of the work per hour.
Find their combined work rate:
Combined rate=1/18+1/36=2+1/36=3/36=1/12
Time taken=1/Combined rate=1/(1/12)=12 hours
Explanation
We calculated each worker’s hourly rate, added them to get the combined rate, and then inverted this combined rate to find the total time required to complete the task together.
Problem 2
Two machines, A and B, produce 18 and 36 units of product respectively in an hour. The factory wants both machines to finish a full production cycle simultaneously. If the LCM of the units produced is achieved, what percentage of each machine’s hourly output is represented by the total production (i.e., LCM of 18 and 36)?
Find the LCM of 18 and 36:
Prime factorization of 18: 18=2×32
Prime factorization of 36: 36=22×32
LCM = 22×32=36
Calculate the percentage of each machine’s hourly output represented by 36:
Machine A produces 18 units per hour, so:
Percentage for Machine A=(36/18×100%)=200%
Machine B produces 36 units per hour, so:
Percentage for Machine B=(36/36×100%)=100%
Explanation
We calculated the LCM of 18 and 36 to determine the cycle time where both machines would align in production. Then, we compared 36 units to each machine's hourly output, calculating each as a percentage of its output.
Problem 3
Verify the relationship of the numbers 18 and 36 using the formula: LCM×GCF=Product of the two numbers
Prime factorization
:
18 = 2×32
36 = 22×32
Calculate the GCF:
GCF = 2 × 32 = 18
Calculate the LCM:
LCM = 36
Verify the formula:
LCM × GCF = 36 × 18 = 648
The product of the two numbers = 18 × 36 = 648
Explanation
The relationship formula holds true since both sides equal 648, confirming that the LCM and GCF calculated for 18 and 36 are correct.
FAQs on the LCM of 18 and 36
1. What is the LCM of 8,18 and 36?
2.What is the LCM of 12,18 and 36?
3.What is the GCF of 18 and 36?
4.What is the LCM of 36 and 16?
5.Prime factorize 36.
6.How can children in Qatar use numbers in everyday life to understand LCM of 18 and 36?
7.What are some fun ways kids in Qatar can practice LCM of 18 and 36 with numbers?
8.What role do numbers and LCM of 18 and 36 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 18 and 36 skills?
Important glossaries for the LCM of 18 and 36
- 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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