The main **objective** of this question is to find the **least common multiple**.

This question **uses** the concept of **least common multiple**. The **least common multiple**, also known as the **lowest common multiple** ofÂ two** integers** **x**Â and** y**, and typically **denoted** by the **notation lcm(x, y).**Â This is indeed the **lowest positive** integer which is **divisible** both by **x** and **y**. This **concept** is used in the** fields** of **arithmetic** and **number theory**.

## Expert Answer

We **have** to find the **least common multiple** for $ 2 $ and $ 4 $.

**First**, we will **find** the **factorization** of $ 2 $, which is:

\[ \space 2 \space = \space 2 \]

Now **the factorization** of 4 is:

\[ \space 2^2 \space = \space 2 \space \times \space 2 \space = \space 4 \]

Thus the **least common** factor is $ 4 $.

## Numerical Answer

The **least common factor** for $ 2 $ **and** $ 4 $ is $ 4 $.

## Example

Find the **least common multiple** for:

- \[ \space 3 \space and \space 9 \]
- \[ \space 4 \space and \space 16 \]
- \[ \space 5 \space and \space 25 \]
- \[ \space 6 \space and \space 36 \]

We **have** to find the **least common multiple** for $ 3 $ and $ 9 $.

**First**, we will **find** the **factorization** of 3, which is:

\[ \space 3 \space = \space 3 \]

Now the **factorization** ofÂ $ 9 $Â is:

\[ \space 3^2 \space = \space 3 \space \times \space 3 \space = \space 9 \]

Thus the** least common** **factor** is $ 9 $.

**Now **we **have** to find the **least common multiple** for $ 4 $ and $ 16 $.

**First**, we will **find** the **factorization** of 4, which is:

\[ \space 2^2\space = \space 2 \space \times \space 2 \space = \space 4 \]

Now the **factorization** ofÂ $ 9 $Â is:

\[ \space 4^2 \space = \space 4\space \times \space 4 \space = \space 16 \]

Thus the** least common** **factor** is:

\[ \space = \space 2 \space \times \space 2 \space \times \space \timesÂ \space 2 \space \times \space 2Â \space = \spaceÂ 16 \]

**Now **we **have** to find the **least common multiple** for $ 5 $ and $ 25 $.

**First**, we will **find** the **factorization** of 5, which is:

\[ \space 5\space = \space 5 \]

Now the **factorization** ofÂ $ 25 $Â is:

\[ \space 5^2 \space = \space 5\space \times \space 5 \space = \space 25\]

Thus the** least common** **factor** is:

\[ \space = \space 5 \space \times \space 5 \spaceÂ = \spaceÂ 25 \]

Now we **have** to find the **least common multiple** for $ 6 $ and $ 36 $.

**First**, we will **find** the **factorization** of 6, which is:

\[ \space 6 \space = \space 2 \space \times \space 3 \space = \space 6Â \]

Now the **factorization** of $ 36 $ is:

\[ \space 6^2 \space = \space 2\space \times \space 3 \spaceÂ \times \space Â 2\space \times \space 3 \space= \space 36 \]

Thus the** least common** **factor** is $ 36 $.