Solve 1/258+1/312+1/112

$$\frac { 1 } { 258 } + \frac { 1 } { 312 } + \frac { 1 } { 112 }$$

Evaluate

$$\frac{3007}{187824}\approx 0.016009669$$

Solution Steps

Least common multiple of 258 and 312 is 13416. Convert \frac{1}{258} and \frac{1}{312} to fractions with denominator 13416.

$$\frac{52}{13416}+\frac{43}{13416}+\frac{1}{112}$$

Since \frac{52}{13416} and \frac{43}{13416} have the same denominator, add them by adding their numerators.

$$\frac{52+43}{13416}+\frac{1}{112}$$

Add 52 and 43 to get 95.

$$\frac{95}{13416}+\frac{1}{112}$$

Least common multiple of 13416 and 112 is 187824. Convert \frac{95}{13416} and \frac{1}{112} to fractions with denominator 187824.

$$\frac{1330}{187824}+\frac{1677}{187824}$$

Since \frac{1330}{187824} and \frac{1677}{187824} have the same denominator, add them by adding their numerators.

$$\frac{1330+1677}{187824}$$

Add 1330 and 1677 to get 3007.

$$\frac{3007}{187824}$$

Factor

$$\frac{31 \cdot 97}{2 ^ {4} \cdot 3 \cdot 7 \cdot 13 \cdot 43} = 0.016009668625947694$$