166 LearnersLast updated on May 26th, 2025
LCM of 80, 85, and 90
LCM of any two numbers is the least common multiple of two numbers. In our daily life, LCM is used for scheduling events, as distributing any items among others. In this topic, we will learn more about LCM of 80, 85, and 90.
What is the LCM of 80, 85 and 90
The common multiples of 80, 85, and 90 is 12240. Here, we will learn about the LCM of 3 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 80, 85, and 90?
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 80, 85, and 90 using the listing multiple method
Listing multiples can be a tedious method for finding the LCM. Here, the listing of multiples for all these 3 numbers is noted -
- Multiples of 80:80, 160, 240, 320, 400, 480, ……12240
- Multiples of 85:85, 170, 225, 340, 425…….12240
- Multiples of 90:90, 180, 270, 360, 450, ……..12240
Ascertain the smallest multiple from the listed method.
Then we can see that out of 80, 85, and 90, 12240 is the smallest common number that is present in them. So we see that 12240 is the LCM of 80, 85, and 90.
LCM of 80, 85, and 90 Using Prime Factorization
The product of the highest power of prime factors of 80, 85, and 90 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 80: 24 × 5
Prime factorization of 85: 5 × 17
Prime factorization of 90: 2 × 32 × 3 × 5
- Multiplying the highest power of prime factors: 24 × 32 × 51 × 17 → 16 × 9 × 5 × 17 = 12240
- LCM of 80, 85, and 90 is 12240.
LCM of 80,85 and 90 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 80, 85, and 90 by 2. The results are 40, 85, and 45.
Step 3: As 40 is divisible by 2, again the divisor is 2. Dividing 40, 85, and 45 by 2. Now the remainder is 20, 85, and 45.
Step 4: Continue dividing the numbers with the smallest prime number until all numbers are reduced to 1.
The divisors are 2, 2, 2, 2, 3, 3, 5, 17. LCM of 80, 85, and 90 is the product of divisors.
Hence, the LCM of (80, 85, and 90) = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 17 = 12240
Common Mistakes and How to Avoid Them in LCM of 80, 85, and 90
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 80, 85, and 90 Examples
Problem 1
Find the smallest number that is divisible by 80,85 and 90 exactly.
Multiples of 80,85 and 90
Multiples of 80:80, 160, 240, 320, 400, 480, ……12240
Multiples of 85:85, 170, 225, 340, 425, …….12240
Multiples of 90:90, 180, 270, 360, 450, ……..12240
Here, the LCM of 45 and 60 is 180
Explanation
So we get the LCM of 80,85 and 90 is 12240. That means The smallest number that both 80,85 and 90 can divide into perfectly.
Problem 2
You organize two different events. One event repeats every 80 days, the other event repeats every 90 days, you want to know, how often both events will occur on the same day?
By prime factorization :
80: 24 × 5
90: 2 × 32 × 5
LCM = 24 × 3 2 × 5 = 16 × 9 × 5 = 720
Explanation
Both events will occur on the same day after 720 days. So here, the first event starts on January 1st. The next time both events will happen on the same day will be in 720 days.
Problem 3
The school bus picks up students every 80 minutes. And another bus picks up students every 90 minutes if both buses pick up students at 8: 00 AM. when they both pick up students at the same time again?
80 = 2 4 × 5
90=2 x 3 2 × 5
LCM = 2 4 × 32 × 5 =16 × 9 × 5 = 720
Explanation
So both buses will pick up students at the same time again after 720 minutes, or 12 hours. If they pick up students at 8:00 AM. They will pick up the students again at 8:00 pm.
FAQ on LCM of 80, 85, and 90
1.What is the GCF of 80, 85, and 90?
2.What is the LCM of 80 and 85?
3.What is the LCM of 50, 80 and 90?
4.What is the LCM of 80, 90 and 75?
5.What is the LCM of 30, 36 and 40?
6.How can children in Thailand use numbers in everyday life to understand LCM of 80, 85, and 90?
7.What are some fun ways kids in Thailand can practice LCM of 80, 85, and 90 with numbers?
8.What role do numbers and LCM of 80, 85, and 90 play in helping children in Thailand develop problem-solving skills?
9.How can families in Thailand create number-rich environments to improve LCM of 80, 85, and 90 skills?
Important Glossaries For LCM Of 80, 85, and 90.
- 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 Thailand
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.
