4.3.2 Determine the lowest common multiple (LCM) of 252 and 360 . $$ \qquad $$ You are given the following information.

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To determine the **Lowest Common Multiple (LCM)** of **252** and **360**, we'll use the **prime factorization method**. Here's a step-by-step guide:

### Step 1: Prime Factorization

**1. Factorize 252:**
$$
252 = 2^2 \times 3^2 \times 7
$$
- $$252 \div 2 = 126$$
- $$126 \div 2 = 63$$
- $$63 \div 3 = 21$$
- $$21 \div 3 = 7$$

**2. Factorize 360:**
$$
360 = 2^3 \times 3^2 \times 5
$$
- $$360 \div 2 = 180$$
- $$180 \div 2 = 90$$
- $$90 \div 2 = 45$$
- $$45 \div 3 = 15$$
- $$15 \div 3 = 5$$

### Step 2: Identify the Highest Powers of All Prime Factors

List all the prime factors from both numbers and choose the highest exponent for each:

- **2:** Highest power is $$2^3$$ (from 360)
- **3:** Highest power is $$3^2$$ (common in both)
- **5:** Present only in 360 as $$5^1$$
- **7:** Present only in 252 as $$7^1$$

### Step 3: Multiply These Highest Powers Together

$$
\text{LCM} = 2^3 \times 3^2 \times 5 \times 7
$$
$$
\text{LCM} = 8 \times 9 \times 5 \times 7
$$
$$
\text{LCM} = 72 \times 35
$$
$$
\text{LCM} = 2520
$$

### Conclusion

The **Lowest Common Multiple (LCM)** of **252** and **360** is **2520**.
The Lowest Common Multiple (LCM) of 252 and 360 is 2520.

4.3.2 Determine the lowest common multiple (LCM) of 252 and 360 . \( \qquad \) You are given the following information.

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