We are asked to
find the least common denominator (LCD) for the fractions in this expression:
$$
\frac{5}{6} + \frac{2}{5} + \frac{3}{8}
$$
---
🔍 Step 1: Identify the denominators
The denominators are:
- 6
- 5
- 8
We need to find the
least common denominator, which is the
least common multiple (LCM) of these three numbers.
---
🔢 Step 2: Find the LCM of 6, 5, and 8
We'll use
prime factorization:
- $6 = 2 \times 3$
- $5 = 5$ (prime)
- $8 = 2^3$
Now, take the
highest power of each prime that appears:
- $2^3$ (from 8)
- $3^1$ (from 6)
- $5^1$ (from 5)
Now multiply them:
$$
2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120
$$
✔ So, the
least common denominator is 120.
---
✔ Final Answer:
$$
\boxed{120}
$$
This means we can rewrite all fractions with denominator 120 to add them easily. But since the question only asks for the
least common denominator, we're done!
Parent Tip: Review the logic above to help your child master the concept of common denominator math.
