Finding the LCM of 0.9, 3.7, and 0.54

To find the Least Common Multiple (LCM) of decimal numbers, we first convert them into fractions with a common denominator.

Step 1: Convert Decimals to Fractions

The given numbers are 0.9, 3.7, and 0.54.

• \(0.9 = \frac{9}{10}\)
• \(3.7 = \frac{37}{10}\)
• \(0.54 = \frac{54}{100}\)

Step 2: Find a Common Denominator

The denominators are 10, 10, and 100. The least common denominator is 100.

Convert the fractions to have the denominator 100:

• \(\frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100}\)
• \(\frac{37}{10} = \frac{37 \times 10}{10 \times 10} = \frac{370}{100}\)
• \(\frac{54}{100}\) remains the same.

The fractions are now \(\frac{90}{100}\), \(\frac{370}{100}\), and \(\frac{54}{100}\).

Step 3: Calculate LCM of Numerators

Find the LCM of the numerators: 90, 370, and 54.

Prime factorization:

• \(90 = 2 \times 3^2 \times 5\)
• \(370 = 2 \times 5 \times 37\)
• \(54 = 2 \times 3^3\)

The LCM is the product of the highest powers of all prime factors involved:

LCM\((90, 370, 54) = 2^1 \times 3^3 \times 5^1 \times 37^1 = 2 \times 27 \times 5 \times 37 = 9990\)

Step 4: Calculate the Final LCM

Divide the LCM of the numerators by the common denominator:

LCM = \(\frac{9990}{100} = 99.9\)

Therefore, the LCM of 0.9, 3.7, and 0.54 is 99.9.