1. **Problem statement:** We have two numbers, 3090 and 1854, and we want to find their greatest common divisor (GCD) and least common multiple (LCM). 2. **Formula and rules:** - The GCD of two numbers is the largest number that divides both without leaving a remainder. - The LCM of two numbers is the smallest number that is a multiple of both. - Important relation: $$\text{GCD}(a,b) \times \text{LCM}(a,b) = a \times b$$ 3. **Step 1: Find the GCD of 3090 and 1854 using the Euclidean algorithm:** - Compute $$3090 \div 1854 = 1$$ remainder $$3090 - 1854 = 1236$$ - Compute $$1854 \div 1236 = 1$$ remainder $$1854 - 1236 = 618$$ - Compute $$1236 \div 618 = 2$$ remainder $$1236 - 2 \times 618 = 0$$ - Since the remainder is 0, the GCD is the last non-zero remainder, which is $$618$$. 4. **Step 2: Find the LCM using the relation:** - Calculate $$\text{LCM} = \frac{3090 \times 1854}{618}$$ - Simplify numerator: $$3090 \times 1854 = 5728860$$ - Divide: $$\frac{5728860}{618} = 9270$$ 5. **Final answers:** - GCD(3090, 1854) = $$618$$ - LCM(3090, 1854) = $$9270$$