# How to Find LCM and HCF ?

How to Calculate Least Common Multiple (LCM) and Highest Common Factor (HCF)?

## Highest Common Factor and Least Common Multiple Calculation

The least common multiple is the smallest positive integer which is multiple of two or more numbers. It is denoted by **LCM**. It is also called as **smallest/lowest common multiple.**

The largest common factor of two or more numbers is called as **highest
common factor. **It is denoted by **HCF**. It is also known as **GCF (Greatest Common Factor)** or **GCD (Greatest Common Divisor)**. Learn here how to find LCM and HCF with simple steps.

**Example to Find LCM :**

Let us consider an example,

Find LCM of 15 and 24.

**Step 1:** Find the prime factors of these two numbers.

Prime Factors of 15 = 3 x 5

Prime Factors of 24 = 2 x 2 x 2 x 3

**Step 2:** Identify the most repeated numbers in prime factorization.

Prime Factors of 15 = **3**x**5**

Prime Factors of 24 = **2**x**2**x**2**x 3

The number 3 appears once in prime factorization of 15 and 24. So, let us take one 3 in common for both 15 and 24.

The number 2 appears thrice in prime factorization of 24. So, all three 2 is considered.

And the number 5 appears once in prime factorization of 15.

**Step 3:** Multiply all the numbers which is in bold font style,

The product is,

**3**x**5****x2**x**2**x**2 = 15 x 8 = 120**

So the LCM of 15 and 24 is **120**

**Example to Find HCF :**

HCF of 12 and 18.

**Step 1: **Find the prime factors of these two numbers

Prime factors of 12 = 2 x 2 x 3

Prime factors of 18 = 2 x 3 x 3

**Step 2: **Identify the common factors of 12 and 18

2 and 3 are the common factors of 12 and 18.

**Step 3: **Identify the highest factor among the common factors.

Here **3** is the highest common factor.

Learn to find least common multiple of numbers using GCD with our how to calculate LCM tutorial.

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