Find the LCM of decimal numbers by scaling to integers: LCM of 3.0, 0.09, and 2.7. Show the scaling and factorization steps.

Introduction / Context:
Least Common Multiple (LCM) for decimals is easiest to compute by converting all numbers to integers with a common power-of-ten multiplier, finding the LCM of those integers, then scaling back. This ensures exactness without floating-point errors.

Given Data / Assumptions:

• Numbers: 3.0, 0.09, 2.7
• Use a common scaling factor of 100 to clear two decimal places uniformly.

Concept / Approach:
Multiply each value by 100: 3.0 → 300; 0.09 → 9; 2.7 → 270. Find LCM(300, 9, 270) as integers. Then divide the result by 100 to restore the decimal scale.

Step-by-Step Solution:
Factorize: 300 = 2^2 * 3 * 5^2; 9 = 3^2; 270 = 2 * 3^3 * 5.LCM uses highest powers: 2^2, 3^3, 5^2.Compute LCM: 4 * 27 * 25 = 2700.Scale back by 100: 2700 ÷ 100 = 27.

Verification / Alternative check:
27 ÷ 3.0 = 9 (integer), 27 ÷ 0.09 = 300 (integer), 27 ÷ 2.7 = 10 (integer). Hence 27 is a common multiple and is least by construction.

Why Other Options Are Wrong:

• 2.7, 0.27, 0.027, 0.9: These are fractions of 27 and fail to be multiples of 0.09 simultaneously or to satisfy all three divisibility checks.

Common Pitfalls:
Using different scaling factors for each number or forgetting to scale back after computing the integer LCM.

Final Answer:
27