Solve 1/frac{1{72}-1/90}

$$\frac { 1 } { \frac { 1 } { 72 } - \frac { 1 } { 90 } }$$

Evaluate

$$360$$

Solution Steps

Least common multiple of 72 and 90 is 360. Convert \frac{1}{72} and \frac{1}{90} to fractions with denominator 360.

$$\frac{1}{\frac{5}{360}-\frac{4}{360}}$$

Since \frac{5}{360} and \frac{4}{360} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{\frac{5-4}{360}}$$

Subtract 4 from 5 to get 1.

$$\frac{1}{\frac{1}{360}}$$

Divide 1 by \frac{1}{360} by multiplying 1 by the reciprocal of \frac{1}{360}.

$$1\times 360$$

Multiply 1 and 360 to get 360.

$$360$$

Factor

$$2^{3}\times 3^{2}\times 5$$