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To find the L.C.M. of decimal numbers like 3, 2.7, and 0.09, we follow these steps:
✅ Step 1: Remove decimals by multiplying all numbers to make them integers.
The highest number of decimal places is 2 (in 0.09), so multiply all numbers by 100:
3 × 100 = 300
2.7 × 100 = 270
0.09 × 100 = 9
Now find the LCM of: 300, 270, and 9
✅ Step 2: Find the LCM of 300, 270, and 9
Prime factorization:
300 = 2² × 3 × 5²
270 = 2 × 3³ × 5
9 = 3²
Take the highest powers of each prime factor:
2²
3³
5²
LCM = 2² × 3³ × 5² = 4 × 27 × 25 = 2700
—
✅ Step 3: Since we multiplied each number by 100 earlier, now divide the result by 100:
LCM = 2700 ÷ 100 = 27
—
✅ Final Answer: The L.C.M. of 3, 2.7 and 0.09 is 27.