Let's solve each problem step by step to find the
Least Common Multiple (LCM) for each set of numbers. The LCM is the smallest number that is a multiple of both (or all) given numbers.
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1. 2, 5
-
Multiples of 2:
$2, 4, 6, 8, 10, 12, 14, 16, 18, 20, \dots$
-
Multiples of 5:
$5, 10, 15, 20, 25, \dots$
-
Common Multiples:
Numbers that appear in both lists: $10, 20, 30, \dots$
-
LCM (2, 5) =
10 ← smallest common multiple
---
2. 4, 6
-
Multiples of 4:
$4, 8, 12, 16, 20, 24, 28, 32, 36, \dots$
-
Multiples of 6:
$6, 12, 18, 24, 30, 36, \dots$
-
Common Multiples:
$12, 24, 36, \dots$
-
LCM (4, 6) =
12
---
3. 6, 9
-
Multiples of 6:
$6, 12, 18, 24, 30, 36, \dots$
-
Multiples of 9:
$9, 18, 27, 36, 45, \dots$
-
Common Multiples:
$18, 36, \dots$
-
LCM (6, 9) =
18
---
4. 12, 6
-
Multiples of 12:
$12, 24, 36, 48, \dots$
-
Multiples of 6:
$6, 12, 18, 24, 30, 36, \dots$
-
Common Multiples:
$12, 24, 36, \dots$
-
LCM (12, 6) =
12 ← since 12 is a multiple of 6
---
5. 10, 20
-
Multiples of 10:
$10, 20, 30, 40, 50, \dots$
-
Multiples of 20:
$20, 40, 60, \dots$
-
Common Multiples:
$20, 40, 60, \dots$
-
LCM (10, 20) =
20 ← since 20 is a multiple of 10
---
✔ Final Answers:
1. LCM (2, 5) =
10
2. LCM (4, 6) =
12
3. LCM (6, 9) =
18
4. LCM (12, 6) =
12
5. LCM (10, 20) =
20
---
🔍 Explanation:
To find the LCM:
- List multiples of each number.
- Identify common multiples.
- Choose the smallest one.
Alternatively, you can use prime factorization or the formula:
$$
\text{LCM}(a,b) = \frac{a \times b}{\text{GCF}(a,b)}
$$
But listing multiples is straightforward for small numbers.
Let me know if you'd like to see the prime factorization method!
Parent Tip: Review the logic above to help your child master the concept of least common multiple practice worksheet.
