Let’s solve this step by step.
We are given the equation:
> x/3 + 1/2 = (3x + 1)/6
And we’re asked to find the
LCD — which stands for
Least Common Denominator.
The LCD is the smallest number that all the denominators in the equation can divide into evenly.
Look at the denominators in the equation:
- First term: denominator is
3
- Second term: denominator is
2
- Right side: denominator is
6
So we need the least common denominator of
3, 2, and 6.
Let’s list multiples:
- Multiples of 3: 3, 6, 9, 12...
- Multiples of 2: 2, 4, 6, 8...
- Multiples of 6: 6, 12, 18...
The smallest number that appears in all three lists? →
6
Also, notice that 6 is already a multiple of both 3 and 2:
- 6 ÷ 3 = 2
✔
- 6 ÷ 2 = 3
✔
- 6 ÷ 6 = 1
✔
So yes — the LCD is
6.
You don’t even need to solve the whole equation to answer this question — it’s just asking for the LCD of the fractions involved.
Final Answer:
6
Parent Tip: Review the logic above to help your child master the concept of solving rational equations.
