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Find the Least Common Denominator

Students learn to identify the least common multiple of two denominators to use as a common denominator when adding or subtracting fractions. Students practice listing multiples and identifying the smallest shared multiple.

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Find the Least Common Denominator

Grade 5 · Adding and Subtracting Fractions with Unlike Denominators · question 1 of 3

0 of 20

20 rungs. A star at the top.

The least common denominator of 1/2 and 1/10 is

How it is taught

0:00 of 3:16

A common denominator is a shared bottom for two fractions.

The least one is the smallest shared multiple of the bottoms.

Read it: Make one cut, then count

1/5 and 3/10 are cut differently: one bar in fifths, one in tenths. Cut each fifth into 2 and 1/5 is 2/10. Now the pieces line up: 2/10 + 3/10 = 5/10, which is 1/2.

  1. Find a cut both bottom numbers go into: 5 and 10 both go into 10.
  2. Write each fraction in that cut: 1/5 is 2/10, and 3/10 stays 3/10.
  3. Add or take away the top numbers and keep the cut: 2/10 + 3/10 = 5/10, which is 1/2.

Pieces of different sizes cannot be counted together, so both bars are cut into the same pieces first.

Cutting a piece into smaller pieces does not change the amount: 1/5 and 2/10 shade the same part of a bar.

The least common denominator is the smallest cut both go into, so its pieces are the biggest that line up.

To add or subtract fractions with different denominators, write both in a common denominator, then add or subtract the numerators.

Adding the tops and the bottoms: 1/5 + 3/10 = 4/15.

4/15 is less than 3/10 alone, because fifteenths are smaller pieces. Cut both into tenths: 2/10 + 3/10 = 5/10, which is 1/2.

The least common denominator of 1/2 and 1/3 is ___ — 6. Cut both bars into 6 (sixths): 2 and 3 both go into 6, and no smaller number works.

LCD of 1/4 and 1/6

How can we add one-fourth and one-sixth? First, we need a common denominator.

The denominators four and six are different. We need a number that BOTH four and six divide into evenly.

Let's list the multiples of four: four, eight, twelve, sixteen, twenty.

Now the multiples of six: six, twelve, eighteen, twenty-four.

Look closely at the fours — there's twelve.

And in the sixes — there's twelve again! It shows up in both lists.

Twelve is the smallest number that appears in both lists. That makes it the least common multiple.

So the least common denominator of one-fourth and one-sixth is twelve. Now we can rewrite both fractions with twelve on the bottom!

What's the LCD of 14 and 16?14+16We need a multiple shared by 4 AND 6Find the smallest shared multiple of 4 and 6Multiples of 4:48121620,,,,Multiples of 6:6121824,,,Smallest shared multiple = 12LCD of 14 and 16 is 12Now both fractions can share denominator 12LCD12of 14 and 16
Grade 5 · Finding the smallest shared denominator

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
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Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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