133 LearnersLast updated on May 26th, 2025
LCM of 10 and 18
LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, and distributing any items among others. In this topic, we will learn more about LCM of 10 and 18.
What is the LCM of 10 and 18
The common multiples\ of 10 and 18 is 90. Here, we will learn about the LCM of 2 numbers. Children learn about LCM at younger ages. Here, we will discuss the methods used for finding out LCM.
How to find the LCM of 10 and 18?
Out of many methods, prime factorization method is widely used for its easy approach. Here, we will learn about other methods as well. A few commonly used methods are as follows -
- Listing Of Multiples
- Prime Factorization
- Division Method
LCM of 10 and 18 Using Listing the Multiplies
Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 2 numbers is noted -
- Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80,90
- Multiples of 18:18, 36, 54, 72, 90
Then we can see that out of 10 and 18, 90 is the smallest common number that is present in them. So we see that 90 is the LCM of 10 and 18.
LCM of 10 and 18 Using Prime Factorization
The product of the highest power of prime factors of 10 and 18 is the LCM of these numbers. So let us look at it step by step to understand it better.
Breaking the given numbers into their prime factors.
Prime factorization of 10: 2 × 5
Prime factorization of 18: 2 × 32
Multiplying the highest power of prime factors: 2 × 32 × 51 → 2 × 9 × 5 = 90
LCM of 10 and 18 is 90.
LCM of 10 and 18 Using Division Method
In this method, we will be dividing the given numbers with the common prime factors until all numbers are reduced to 1. Let us look at this step by step and make it easy for the children to learn it.
Step 1: Arrange the number in a sequence, divisors, and the numbers are on the left and right sides respectively.
Step 2: For finding the divisor, it is always the smallest common prime factor. Here, the smallest common prime factor is 2. Dividing 10 and 18 by 2. The result is 5 and 9.
Step 3: As 9 is divisible by 3, the divisor is 3. Dividing 5 and 9 by 3. Now the result is 5 and 3.
Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.
The divisors are 2, 3, 3, 5. LCM of 10 and 18 is the product of divisors.
Hence, the LCM of (10 and 18) = 2 × 3 × 3 × 5 = 90
Common Mistakes and How to Avoid Them in LCM of 10 and 18
There are some common mistakes that are made by children while solving a problem on LCM. Let us look at some of these mistakes and how we can help children to avoid these mistakes.
Mistake 1
Confusing factors and multiples.
Students used to confuse factors and multiples. To avoid confusion, students need to understand the concept of multiples and factors. Multiplies of a number are the product of the number with whole numbers, whereas factors of the number are the numbers which can evenly divide the number. For example, 1, 2, 3, 4, 6, and 12 are the factors of 12; whereas 12, 24, 36, 48, 60,… are the multiples of 12.
LCM of 10 and 18 Example
Problem 1
The product of the two numbers is 180 and their GCF is 2, what is their LCM?
Given :
The product of two numbers is 180
GCF = 2
So the LCM of two numbers,
LCM = product of the number / GCF
LCM = 180/2 =90
So the LCM of two numbers is 90.
Explanation
Here, also given the product of the two numbers and GCF. When we find the LCM, we divide the product of the numbers by GCD. Then we get the LCM of 90.
Problem 2
Two alarms ring at intervals of 10 and 18 minutes, respectively. If both alarms ring together at 8:00 AM, when will they ring together?
by prime factorization :
10 = 2 × 5
18 = 2 × 32
LCM = 2 × 3 × 3 × 5 =90
Explanation
When we find they will be together again, first we calculate the LCM of 10 and 18. We get the LCM of 10 and 18 is 90. So they will be together again in 90 minutes, or at 9: 30 AM.
Problem 3
A school schedules science class every 10 days and math class every 18 days. If both classes are held on the same day today, when will both classes happen on the same day again?
We find the LCM of 10 and 18 to determine when both events will align.
The LCM of 10 and 18 is 90
Explanation
Both classes will be held on the same day again in 90 days.
FAQs on LCM of 10 and 18
1.What is the LCM of 10, 18, and 20?
2.How do you find the LCM of 10 and 18?
3.What is the LCM of 6 and 8?
4.What is the LCM of 10 and 8?
5.What is the LCM of 12 and 18?
6.How can children in United States use numbers in everyday life to understand LCM of 10 and 18?
7.What are some fun ways kids in United States can practice LCM of 10 and 18 with numbers?
8.What role do numbers and LCM of 10 and 18 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve LCM of 10 and 18 skills?
Important Glossaries of LCM of 10 and 18
- Factor: A number that will divide two or more numbers, leaving no remainder. For 18 and 24 we have 6 as a common factor, it means both 18 and 24 can be divisible by 6.
- Prime Factorization: When a number can be represented as the factors of prime numbers, it is called prime factorization. The prime factorization of 18 for example is 2×3×3.
- Greatest Common Factor (GCF): GCF is the greatest factor that is common in the given numbers. For example, the GCF of 5, 10, and 15 is 5. Because the common factors of 5 and 10 are 1 and 5.
- Division Method: In the division method, the numbers are divided by the smallest common prime factor till the numbers are reduced to 1.
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About BrightChamps in United States
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.
