Least Common Denominator - The Key to Adding & Subtracting!
Students will find the Least Common Denominator (LCD) for uncommon fractions like 1/5, 1/6, 1/7, 1/8, 1/9, and 1/10 with 80% accuracy.
Section 1 of 5
The LCD is the smallest number that ALL the denominators can divide into evenly.
Why do we need it? To add or subtract fractions, they MUST have the same denominator!
You can't add 1/5 + 1/6 directly because fifths and sixths are different sizes!
We need to find a common "language" - the LCD!
With your partner: What number can BOTH 5 and 10 divide into?
✅ 10! Because 5 × 2 = 10 and 10 × 1 = 10
Write out multiples of each denominator until you find a match!
Multiples of 5: 5, 10, 15, 20, 25, 30, 35...
Multiples of 6: 6, 12, 18, 24, 30, 36...
LCD = 30 ✓
Sometimes one denominator is already a multiple of the other!
Is 10 a multiple of 5? YES! (5 × 2 = 10)
LCD = 10 ✓
When denominators have NO common factors, multiply them!
7 and 9 have no common factors
7 × 9 = 63
LCD = 63 ✓
| Fractions | LCD | How? |
|---|---|---|
| 1/5 and 1/6 | 30 | 5 × 6 = 30 |
| 1/5 and 1/10 | 10 | 10 is multiple of 5 |
| 1/6 and 1/8 | 24 | Multiples: 24 |
| 1/6 and 1/9 | 18 | Multiples: 18 |
| 1/7 and 1/8 | 56 | 7 × 8 = 56 |
| 1/8 and 1/10 | 40 | Multiples: 40 |
| 1/9 and 1/10 | 90 | 9 × 10 = 90 |