19. State the smallest integer that is divisible by both 20 and 45.

Question

UpStudy AI · Accepted Answer

To find the smallest integer divisible by both 20 and 45, we need to determine the **Least Common Multiple (LCM)** of these two numbers.

**Step 1: Prime Factorization**

1. **Factorize 20 and 45:**
   - $$ 20 = 2^2 \times 5 $$
   - $$ 45 = 3^2 \times 5 $$

**Step 2: Determine the LCM**

The LCM is found by taking the highest power of each prime that appears in the factorization of both numbers.

- **For 2:** The highest power is $$ 2^2 $$ (from 20).
- **For 3:** The highest power is $$ 3^2 $$ (from 45).
- **For 5:** The highest power is $$ 5 $$ (common to both).

So, the LCM is:
$$
LCM = 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180
$$

**Conclusion:**

The smallest integer that is divisible by both 20 and 45 is **180**.
The smallest integer divisible by both 20 and 45 is 180.

19. State the smallest integer that is divisible by both 20 and 45.

Real Tutor Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Arithmetic Questions