\[\frac{1}{9}+\frac{7}{30}+\frac{1}{6}\]

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Find the Least Common Denominator (LCD) of

\frac{1}{9},\frac{7}{30},\frac{1}{6}

. In other words, find the Least Common Multiple (LCM) of

9,30,6

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 9

: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...

Multiples of 30

: 30, 60, 90, ...

Multiples of 6

: 6, 12, 18, ... , 78, 84, 90, ...

Find the smallest number that is shared by all rows above. This is the LCM.

LCM =

90

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 9

: 3, 3

Prime Factors of 30

: 2, 3, 5

Prime Factors of 6

: 2, 3

Find the union of these primes.

2,3,3,5

Multiply these numbers:

2\times 3\times 3\times 5=90

. This is the LCM.

LCM =

90

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LCD =

90

Make the denominators the same as the LCD.

\frac{1\times 10}{9\times 10}+\frac{7\times 3}{30\times 3}+\frac{1\times 15}{6\times 15}

Simplify. Denominators are now the same.

\frac{10}{90}+\frac{21}{90}+\frac{15}{90}

Join the denominators.

\frac{10+21+15}{90}

Simplify.

\frac{46}{90}

Simplify.

\frac{23}{45}

Done

Decimal Form: 0.511111

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