Let's solve the problem step by step using the
century chart (a grid of numbers from 1 to 100) as described in the image.
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🔍 Goal:
Find the
Lowest Common Multiple (LCM) of
6 and 9 using a century chart.
We are told:
- Shade the
multiples of 6.
- Underline the
multiples of 9.
- The
common multiples are the numbers that are
both shaded and underlined.
- The
first such number is the
LCM.
---
✔ Step 1: Find Multiples of 6 (Shade them)
Multiples of 6 are:
> 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
So, we would shade these numbers on the chart.
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✔ Step 2: Find Multiples of 9 (Underline them)
Multiples of 9 are:
> 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
So, we underline these numbers.
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✔ Step 3: Find Common Multiples (Shaded AND Underlined)
Now look for numbers that appear in
both lists:
- Multiples of 6: 6, 12,
18, 24,
36, 42, 48,
54, 60,
72, 78, 84,
90, 96
- Multiples of 9: 9,
18, 27,
36, 45,
54, 63,
72, 81,
90, 99
Common numbers:
✔ 18, 36, 54, 72, 90
These are the
common multiples.
---
✔ Step 4: Identify the Lowest Common Multiple
The
smallest number in the list of common multiples is:
>
18
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✔ Final Answer:
>
The lowest common multiple (LCM) of 6 and 9 is 18.
This matches what’s stated in the image: *"The lowest common multiple is 18 — the first shaded and underlined number."*
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🧠 Bonus: Why does this work?
- The LCM is the smallest number that is divisible by both numbers.
- By listing multiples, we find where they overlap.
- Using the chart visually helps students see patterns and understand the concept.
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✔ Summary:
-
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96
-
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
-
Common multiples: 18, 36, 54, 72, 90
-
LCM = 18
✔ Answer: 18
Parent Tip: Review the logic above to help your child master the concept of common multiples chart.
