The image shows a hand-drawn comparison between finding the
Greatest Common Factor (GCF) and the
Least Common Multiple (LCM) of two numbers:
24 and
40. Let's go through both methods step by step and explain the solution.
---
🔹 Step 1: Prime Factorization
We start by breaking down both numbers into their prime factors.
#### For 24:
- 24 ÷ 2 = 12
- 12 ÷ 2 = 6
- 6 ÷ 2 = 3
- 3 ÷ 3 = 1
So,
24 = 2 × 2 × 2 × 3 = 2³ × 3
#### For 40:
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 ÷ 5 = 1
So,
40 = 2 × 2 × 2 × 5 = 2³ × 5
---
🔹 Step 2: Find GCF (Greatest Common Factor)
The GCF is the product of the
common prime factors with the
lowest powers.
- Both have
2³ (i.e., 2 × 2 × 2)
- But 24 has a
3, and 40 has a
5 — these are not shared.
✔ So, GCF =
2³ = 8
This matches what’s shown in the image:
> GCF = 2 × 2 × 2 = 8
✔️ Correct!
---
🔹 Step 3: Find LCM (Least Common Multiple)
The LCM is the product of the
highest powers of all prime factors present in either number.
From above:
- 24 = 2³ × 3
- 40 = 2³ × 5
Now take:
- The highest power of
2: 2³
- The
3 from 24
- The
5 from 40
So,
LCM = 2³ × 3 × 5 = 8 × 3 × 5 =
120
But wait — in the image, the LCM part seems incomplete or unclear. It shows factor trees but doesn't compute the final LCM value.
Let’s complete it:
✔ LCM = 2 × 2 × 2 × 3 × 5 =
120
---
✔ Final Answer:
-
GCF of 24 and 40 = 8
-
LCM of 24 and 40 = 120
---
🧠 Summary of Methods:
| Method | How to Compute |
|-------|----------------|
|
GCF | Multiply
only common prime factors (lowest exponents) |
|
LCM | Multiply
all prime factors (highest exponents) |
---
✔ Verification:
- 24 × 40 = 960
- GCF × LCM = 8 × 120 = 960 → ✔️ Matches!
(This is a useful check:
GCF × LCM = Product of two numbers)
---
📌 Conclusion:
The image correctly computes the
GCF = 8 using prime factorization and common factors.
However, it
does not show the LCM calculation, though the factor trees are correct.
To finish:
>
✔ GCF = 8
>
✔ LCM = 120
Let me know if you'd like this explained visually or with another example!
Parent Tip: Review the logic above to help your child master the concept of math gcf and lcm.
