\[\frac{1}{2}+\frac{1}{3}\]

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Find the Least Common Denominator (LCD) of

\frac{1}{2},\frac{1}{3}

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

2,3

Method 1: By Listing Multiples

List the multiples of each number.

Multiples of 2

: 2, 4, 6, ...

Multiples of 3

: 3, 6, ...

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

LCM =

6

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 2

: 2

Prime Factors of 3

: 3

Find the union of these primes.

2,3

Multiply these numbers:

2\times 3=6

. This is the LCM.

LCM =

6

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LCD =

6

Make the denominators the same as the LCD.

\frac{1\times 3}{2\times 3}+\frac{1\times 2}{3\times 2}

Simplify. Denominators are now the same.

\frac{3}{6}+\frac{2}{6}

Join the denominators.

\frac{3+2}{6}

Simplify.

\frac{5}{6}

Done

Decimal Form: 0.833333

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