Solve 1/21+1/28+1/24+1/36+frac{1}{108}+frac{1}{136}

$$\frac{ 1 }{ 21 } + \frac{ 1 }{ 28 } + \frac{ 1 }{ 24 } + \frac{ 1 }{ 36 } + \frac{ 1 }{ 108 } + \frac{ 1 }{ 136 }$$

Evaluate

$$\frac{311}{1836}\approx 0.169389978$$

Solution Steps

Least common multiple of 21 and 28 is 84. Convert \frac{1}{21} and \frac{1}{28} to fractions with denominator 84.

$$\frac{4}{84}+\frac{3}{84}+\frac{1}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Since \frac{4}{84} and \frac{3}{84} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{84}+\frac{1}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Add 4 and 3 to get 7.

$$\frac{7}{84}+\frac{1}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Reduce the fraction \frac{7}{84} to lowest terms by extracting and canceling out 7.

$$\frac{1}{12}+\frac{1}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Least common multiple of 12 and 24 is 24. Convert \frac{1}{12} and \frac{1}{24} to fractions with denominator 24.

$$\frac{2}{24}+\frac{1}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Since \frac{2}{24} and \frac{1}{24} have the same denominator, add them by adding their numerators.

$$\frac{2+1}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Add 2 and 1 to get 3.

$$\frac{3}{24}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Reduce the fraction \frac{3}{24} to lowest terms by extracting and canceling out 3.

$$\frac{1}{8}+\frac{1}{36}+\frac{1}{108}+\frac{1}{136}$$

Least common multiple of 8 and 36 is 72. Convert \frac{1}{8} and \frac{1}{36} to fractions with denominator 72.

$$\frac{9}{72}+\frac{2}{72}+\frac{1}{108}+\frac{1}{136}$$

Since \frac{9}{72} and \frac{2}{72} have the same denominator, add them by adding their numerators.

$$\frac{9+2}{72}+\frac{1}{108}+\frac{1}{136}$$

Add 9 and 2 to get 11.

$$\frac{11}{72}+\frac{1}{108}+\frac{1}{136}$$

Least common multiple of 72 and 108 is 216. Convert \frac{11}{72} and \frac{1}{108} to fractions with denominator 216.

$$\frac{33}{216}+\frac{2}{216}+\frac{1}{136}$$

Since \frac{33}{216} and \frac{2}{216} have the same denominator, add them by adding their numerators.

$$\frac{33+2}{216}+\frac{1}{136}$$

Add 33 and 2 to get 35.

$$\frac{35}{216}+\frac{1}{136}$$

Least common multiple of 216 and 136 is 3672. Convert \frac{35}{216} and \frac{1}{136} to fractions with denominator 3672.

$$\frac{595}{3672}+\frac{27}{3672}$$

Since \frac{595}{3672} and \frac{27}{3672} have the same denominator, add them by adding their numerators.

$$\frac{595+27}{3672}$$

Add 595 and 27 to get 622.

$$\frac{622}{3672}$$

Reduce the fraction \frac{622}{3672} to lowest terms by extracting and canceling out 2.

$$\frac{311}{1836}$$

Factor

$$\frac{311}{2 ^ {2} \cdot 3 ^ {3} \cdot 17} = 0.16938997821350762$$