Grade 6 Math Worksheet - Least common multiple (LCM) of 3 numbers ... - Free Printable

Problem: Finding the Least Common Multiple (LCM) of Three Numbers

The task is to find the least common multiple (LCM) of three numbers for each set provided in the worksheet. Below, I will solve one example step-by-step and then provide the solutions for all the sets.

---

#### Step-by-Step Solution for One Example:
Let's solve the first set: 14, 21, 7.

1. Prime Factorization:
- 14: $ 14 = 2 \times 7 $
- 21: $ 21 = 3 \times 7 $
- 7: $ 7 = 7 $

2. Identify All Prime Factors:
The prime factors involved are: $ 2, 3, 7 $.

3. Take the Highest Power of Each Prime Factor:
- For $ 2 $: The highest power is $ 2^1 $ (from 14).
- For $ 3 $: The highest power is $ 3^1 $ (from 21).
- For $ 7 $: The highest power is $ 7^1 $ (from 14, 21, and 7).

4. Calculate the LCM:
$$
\text{LCM} = 2^1 \times 3^1 \times 7^1 = 2 \times 3 \times 7 = 42
$$

So, the LCM of 14, 21, 7 is 42.

---

#### Solutions for All Sets:

Now, let's solve all the sets using the same method.

1. 14, 21, 7
- Prime factors: $ 2, 3, 7 $
- LCM: $ 2^1 \times 3^1 \times 7^1 = 42 $
- Answer: 42

2. 8, 19, 23
- Prime factors: $ 2, 19, 23 $
- LCM: $ 2^3 \times 19^1 \times 23^1 = 8 \times 19 \times 23 = 3536 $
- Answer: 3536

3. 13, 29, 21
- Prime factors: $ 3, 7, 13, 29 $
- LCM: $ 3^1 \times 7^1 \times 13^1 \times 29^1 = 3 \times 7 \times 13 \times 29 = 7917 $
- Answer: 7917

4. 19, 14, 8
- Prime factors: $ 2, 7, 19 $
- LCM: $ 2^3 \times 7^1 \times 19^1 = 8 \times 7 \times 19 = 1064 $
- Answer: 1064

5. 14, 28, 21
- Prime factors: $ 2, 3, 7 $
- LCM: $ 2^2 \times 3^1 \times 7^1 = 4 \times 3 \times 7 = 84 $
- Answer: 84

6. 18, 29, 21
- Prime factors: $ 2, 3, 7, 29 $
- LCM: $ 2^1 \times 3^2 \times 7^1 \times 29^1 = 2 \times 9 \times 7 \times 29 = 3834 $
- Answer: 3834

7. 24, 11, 14
- Prime factors: $ 2, 3, 7, 11 $
- LCM: $ 2^3 \times 3^1 \times 7^1 \times 11^1 = 8 \times 3 \times 7 \times 11 = 1848 $
- Answer: 1848

8. 17, 30, 11
- Prime factors: $ 2, 3, 5, 11, 17 $
- LCM: $ 2^1 \times 3^1 \times 5^1 \times 11^1 \times 17^1 = 2 \times 3 \times 5 \times 11 \times 17 = 5610 $
- Answer: 5610

9. 21, 11, 15
- Prime factors: $ 3, 5, 7, 11 $
- LCM: $ 3^1 \times 5^1 \times 7^1 \times 11^1 = 3 \times 5 \times 7 \times 11 = 1155 $
- Answer: 1155

10. 24, 14, 28
- Prime factors: $ 2, 3, 7 $
- LCM: $ 2^3 \times 3^1 \times 7^1 = 8 \times 3 \times 7 = 168 $
- Answer: 168

11. 9, 27, 2
- Prime factors: $ 2, 3 $
- LCM: $ 2^1 \times 3^3 = 2 \times 27 = 54 $
- Answer: 54

12. 3, 10, 14
- Prime factors: $ 2, 3, 5, 7 $
- LCM: $ 2^1 \times 3^1 \times 5^1 \times 7^1 = 2 \times 3 \times 5 \times 7 = 210 $
- Answer: 210

13. 9, 27, 2
- Prime factors: $ 2, 3 $
- LCM: $ 2^1 \times 3^3 = 2 \times 27 = 54 $
- Answer: 54

14. 14, 17, 12
- Prime factors: $ 2, 3, 7, 17 $
- LCM: $ 2^2 \times 3^1 \times 7^1 \times 17^1 = 4 \times 3 \times 7 \times 17 = 1428 $
- Answer: 1428

---

Final Answers:

$$
\boxed{
\begin{aligned}
&1. 42 \\
&2. 3536 \\
&3. 7917 \\
&4. 1064 \\
&5. 84 \\
&6. 3834 \\
&7. 1848 \\
&8. 5610 \\
&9. 1155 \\
&10. 168 \\
&11. 54 \\
&12. 210 \\
&13. 54 \\
&14. 1428 \\
\end{aligned}
}
$$