Calculating LCM of Decimal Numbers 12.8 and 0.004

To find the Least Common Multiple (LCM) of decimal numbers, we can convert them into integers by multiplying with an appropriate power of 10.

Step 1: Convert Decimals to Integers

Identify the numbers and the maximum number of decimal places:

• The numbers are $12.8$ and $0.004$.
• The number $0.004$ has 3 decimal places.
• Multiply both numbers by $10^3 = 1000$ to eliminate decimals.
• $12.8 \times 1000 = 12800$
• $0.004 \times 1000 = 4$

Step 2: Find LCM of the Integers

Calculate the LCM of the resulting integers, $12800$ and $4$.

• We need the smallest positive integer that is divisible by both $12800$ and $4$.
• Notice that $12800$ is already a multiple of $4$ ($12800 \div 4 = 3200$).
• When one integer is a multiple of another, their LCM is the larger integer.
• Therefore, $LCM(12800, 4) = 12800$.

Step 3: Convert LCM Back to Decimal

Divide the LCM found in Step 2 by the multiplier ($1000$) to get the LCM of the original decimal numbers.

• $LCM(12.8, 0.004) = \frac{LCM(12800, 4)}{1000}$
• $LCM(12.8, 0.004) = \frac{12800}{1000}$
• $LCM(12.8, 0.004) = 12.8$

Alternatively, notice that $12.8$ is directly a multiple of $0.004$ ($12.8 \div 0.004 = 3200$). When one number is a multiple of the other, the LCM is the larger number, which is $12.8$.