1. **State the problem:** Find the least common multiple (LCM) of the numbers 30 and 90. 2. **Recall the formula:** The LCM of two numbers $a$ and $b$ can be found using the formula: $$\text{LCM}(a,b) = \frac{|a \times b|}{\text{GCD}(a,b)}$$ where GCD is the greatest common divisor. 3. **Find the GCD of 30 and 90:** - Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 - Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 - Common factors: 1, 2, 3, 5, 6, 10, 15, 30 - Greatest common factor is 30. 4. **Calculate the LCM:** $$\text{LCM}(30,90) = \frac{30 \times 90}{30}$$ 5. **Simplify the fraction:** $$= \frac{\cancel{30} \times 90}{\cancel{30}} = 90$$ 6. **Conclusion:** The least common multiple of 30 and 90 is 90. **Final answer:** 90