The LCM of the numbers $ 2.5 $ and $ 0.175 $ is:

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Examoogle · Accepted Answer

The correct answer is Option C: 17.5. Convert decimals to fractions: $2.5 = \frac{2500}{1000} = \frac{25}{10}$ and $0.175 = \frac{175}{1000} = \frac{7}{40}$. Express with a common denominator (40): $\frac{100}{40}$ and $\frac{7}{40}$. The LCM is $\frac{	ext{LCM}(100, 7)}{40} = \frac{700}{40} = 17.5$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Convert decimals to fractions: $2.5 = \frac{2500}{1000} = \frac{25}{10}$ and $0.175 = \frac{175}{1000} = \frac{7}{40}$. Express with a common denominator (40): $\frac{100}{40}$ and $\frac{7}{40}$. The LCM is $\frac{	ext{LCM}(100, 7)}{40} = \frac{700}{40} = 17.5$.

Formula Used: $$	ext{LCM} = \frac{	ext{LCM of numerators}}{	ext{HCF of denominators}}$$

Given: Two numbers 2.5 and 0.175.

Steps: Convert decimals to fractions: Convert $2.5$ and $0.175$ into fractions with a common denominator of $1000$: $2.5 = \frac{2500}{1000}$ and $0.175 = \frac{175}{1000}$.. Simplify fractions to common denominator: Simplify the fractions: $\frac{2500}{1000} = \frac{25}{10} = \frac{100}{40}$ and $\frac{175}{1000} = \frac{7}{40}$.. Calculate LCM: Find the LCM of the fractions using the formula: $\frac{	ext{LCM(numerators)}}{	ext{HCF(denominators)}} = \frac{	ext{LCM}(100, 7)}{	ext{HCF}(40, 40)} = \frac{700}{40}$.

Answer: C is correct because the LCM of 2.5 and 0.175 is calculated as 17.5.

Exam Tip: This method of converting decimals to fractions with a common denominator is also highly effective for finding the HCF of decimals.

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