1. **State the problem:** Find the greatest number divisible by both 3.5 and 4.5. 2. **Understand the problem:** To find a number divisible by both 3.5 and 4.5, we need to find the Least Common Multiple (LCM) of these two numbers. 3. **Convert decimals to fractions:** - 3.5 = $\frac{7}{2}$ - 4.5 = $\frac{9}{2}$ 4. **Find the LCM of the fractions:** The LCM of two fractions $\frac{a}{b}$ and $\frac{c}{d}$ is given by: $$\text{LCM} = \frac{\text{LCM}(a,c)}{\text{GCD}(b,d)}$$ 5. **Calculate LCM of numerators 7 and 9:** - Factors of 7: 7 - Factors of 9: 3 \times 3 - LCM(7,9) = 7 \times 3 \times 3 = 63 6. **Calculate GCD of denominators 2 and 2:** - GCD(2,2) = 2 7. **Calculate LCM of 3.5 and 4.5:** $$\text{LCM} = \frac{63}{2} = 31.5$$ 8. **Interpretation:** The smallest positive number divisible by both 3.5 and 4.5 is 31.5. 9. **Greatest number divisible by both:** Since multiples of 31.5 are infinite, the greatest number divisible by both depends on context (e.g., within a range). Without a limit, there is no greatest number. **Final answer:** The least common multiple of 3.5 and 4.5 is $31.5$. There is no greatest number divisible by both without a specified range.