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Last updated on January 8th, 2025

LCM of 80, 85, and 90

Q: What is the GCF of 80, 85, and 90?

Here, the GCF (HCF) is 5. First, we write the factors of each number, then identify the common factors and, then find the greatest common factors

Q: What is the LCM of 80 and 85?

The LCM stands for Least common multiple, So the LCM of 85 and 80 is 1360

Q: What is the LCM of 80, 90 and 75?

The smallest integer that divides the numbers, with no numbers left behind. So the LCM of 80, 90, and 75 is 3600

Q: What is the LCM of 30, 36 and 40?

The LCM of 30, 36, and 40 is 360.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

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

LCM of 80, 85, and 90 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Find the smallest number that is divisible by 80,85 and 90 exactly.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

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?

Explanation

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?

Explanation

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?

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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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.