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127 LearnersLast updated on December 30th, 2024
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.
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?
Explanation
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)?
Explanation
Problem 3
Verify the relationship of the numbers 18 and 36 using the formula: LCM×GCF=Product of the two numbers
Explanation
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.
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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