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.
Similar Questions
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