We are given the expression:
$$
\frac{5}{6} + \frac{2}{5} + \frac{3}{8}
$$
Our goal is to
find the least common denominator (LCD) of these three fractions.
---
Step 1: Identify the denominators
The denominators are:
- 6
- 5
- 8
We need to find the
least common multiple (LCM) of these numbers, because the
LCD is the LCM of the denominators.
---
Step 2: Prime factorization of each number
- $6 = 2 \times 3$
- $5 = 5$ (prime)
- $8 = 2^3$
---
Step 3: Take the highest power of each prime
- For
2: highest power is $2^3$ (from 8)
- For
3: highest power is $3^1$ (from 6)
- For
5: highest power is $5^1$ (from 5)
Now multiply them together:
$$
\text{LCM} = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120
$$
---
✔ Answer:
The
least common denominator is
120.
---
Optional: Convert each fraction to have denominator 120
Just for verification:
- $\frac{5}{6} = \frac{5 \times 20}{6 \times 20} = \frac{100}{120}$
- $\frac{2}{5} = \frac{2 \times 24}{5 \times 24} = \frac{48}{120}$
- $\frac{3}{8} = \frac{3 \times 15}{8 \times 15} = \frac{45}{120}$
Now you can add them:
$$
\frac{100}{120} + \frac{48}{120} + \frac{45}{120} = \frac{193}{120}
$$
But the question only asks for the
least common denominator, which is:
>
✔ 120
Parent Tip: Review the logic above to help your child master the concept of finding lowest common denominator.
