LCM Calculation for Decimal Numbers

To find the Least Common Multiple (LCM) of decimal numbers like 2.72 and 1.44, we convert them to fractions or scaled integers, find the LCM of the integers, and then convert back.

Step 1: Convert Relevant Decimals to Fractions

Focusing on the numbers resulting in the given options, we convert 2.72 and 1.44:

• $2.72 = \frac{272}{100}$
• $1.44 = \frac{144}{100}$

Step 2: Find LCM of Numerators

Find the LCM of the numerators 272 and 144 using prime factorization:

• $272 = 2^4 \times 17$
• $144 = 2^4 \times 3^2$

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

$ LCM(272, 144) = 2^4 \times 3^2 \times 17^1 = 16 \times 9 \times 17 = 2448 $

Step 3: Convert LCM Back to Decimal

Convert the integer LCM back to decimal form by dividing by the common denominator (100):

$ LCM_{decimal} = \frac{2448}{100} = 24.48 $

Thus, the LCM is 24.48.