HCF and LCM Calculator

HCF calculator is a multiservice tool that finds the highest common factor and lowest common factor of the given numbers at the same time. It only needs one input value to find the HCF and LCM simultaneously.

Note: GCF, GCD, and HCF are the same. All names are used to represent a similar method of finding the highest or greatest common factor/divisor.

In this article, we will explain what is HCF with HCF definition, how to find the highest common factor, LCM definition, and how to find LCM of the given numbers.

What is HCF?

What is the Highest common factor? If you are looking for the answer to this question, you are in the right place. HCF stands for highest common factor and LCM stands for least common multiple.

HCF is the greatest integer that divides all numbers and LCM is the smallest integer that is divisible by all numbers.

The above HCF finder lets you find HCF and LCM with more convenience than getting engaged in lengthy calculations. Nonetheless, if you want to learn the handbook method before using the highest common factor calculator, jump to the next section.

How to calculate HCF?

Curious about how to find the HCF? HCF can be calculated using:

• Factoring
• Prime factorization

1. Factoring

Example: Find the HCF of 12 and 15 using factors?

Solution:

Step 1: List all of the factors of the given numbers.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 15: 1, 3, 5, 15

Step 2: Circle or highlight the numbers that exist in the factors of both numbers and should be the greatest common number. In this case, 3 is the largest common number in both of them.

Factors of 12: 1, 2, 3, 4, 6, 12

Factors of 15: 1, 3, 5, 15

So, HCF (12, 15) = 3

If you want to cross-check the answer, place the values in the highest common factor calculator to get the answer.

2. Prime factorization

Example: Find the HCF of 20, 25, and 30 using prime factorization?

Solution:

Step 1: List the prime factors of the given numbers.

Prime factors of 20: 2 × 2 × 5

Prime factors of 25: 5 × 5

Prime factors of 30: 2 × 3 × 5

Step 2: Highlight the numbers that are common in the prime factors of all three numbers.

20: 2 × 2 × 5

25: 5 × 5

30: 2 × 3 × 5

So, HCF (20, 25, 30) = 5

If there is more than one common number, multiply all common numbers to get the HCF. You can verify the answer using the Highest common divisor calculator above.

How to calculate LCM?

Besides using common factor calculator for least common multiples, LCM can be calculated using several methods.

• Prime Factorization
• Prime Factorization using exponents
• List of multiples
• Brute-Force method
• Division Method

1. Prime factorization method

Example: Find LCM of 200, 300, and 400 using prime factorization?
Solution:
Step 1: List the prime factors of the given numbers.
200: 5 × 5 × 2 × 2 × 2 = 5² × 2³
300: 5 × 5 × 2 × 2 × 3 = 5² × 2² × 3

400: 5 × 5 × 2 × 2 × 2 × 2 = 5² × 2⁴
Step 2: To get the LCM, multiply the prime factors. Use the common factors only once when multiplying.

200: 5² × 2³
300: 5² × 2² × 3

400: 5² × 2⁴
5² × 2⁴ × 3 = 1200
So, LCM (200, 300, 400) = 1200

Place the values in the GCD calculator above to validate the answer.

2. List of multiples

Example: Find the LCM of 10 and 15 with the listing multiples method?
Step 1: Write down the multiples of the given numbers.
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80…
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105…
Step 2: Highlight the common multiple in the multiples of given numbers.
10 = 10, 20, 30, 40, 50, 60, 70, 80…
15 = 15, 30, 45, 60, 75, 90, 105…
So, LCM (10, 15) = 30 

Table of HCF(GCF) and LCM:

LCM of 8 and 12	4
LCM of 4 and 10	20
LCM of 10 and 15	30
LCM of 7 and 12	84
LCM of 6 and 8	24
LCM of 9 and 15	45
LCM of 4 and 9	36
HCF of 8 and 12	4
HCF of 28 and 32	4
HCF of 16 and 24	8
HCF of 40 and 48	8
HCF of 72 and 36	36
HCF of 6 and 15	3
HCF of 12 and 18	6