Grade 5 Factoring Worksheets: Lowest Common Multiple (LCM) | Worsheets library... - Free Printable

Problem Description:

The task is to find the Lowest Common Multiple (LCM) for each pair of numbers listed in the worksheet. The LCM of two numbers is the smallest positive integer that is divisible by both numbers.

Solution Approach:

To find the LCM of two numbers, we can use the following steps:
1. Prime Factorization: Break down each number into its prime factors.
2. Identify All Prime Factors: List all the prime factors of both numbers, ensuring each factor appears as many times as it does in either number.
3. Multiply the Factors: Multiply these prime factors together to get the LCM.

Alternatively, you can use the formula:
\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}
\]
where GCD is the Greatest Common Divisor.

Step-by-Step Solutions:

#### 1. \(4\) and \(22\)
- Prime factorization:
- \(4 = 2^2\)
- \(22 = 2 \times 11\)
- Combine the factors: \(2^2 \times 11 = 4 \times 11 = 44\)
- LCM: \(44\)

#### 2. \(6\) and \(24\)
- Prime factorization:
- \(6 = 2 \times 3\)
- \(24 = 2^3 \times 3\)
- Combine the factors: \(2^3 \times 3 = 8 \times 3 = 24\)
- LCM: \(24\)

#### 3. \(8\) and \(6\)
- Prime factorization:
- \(8 = 2^3\)
- \(6 = 2 \times 3\)
- Combine the factors: \(2^3 \times 3 = 8 \times 3 = 24\)
- LCM: \(24\)

#### 4. \(3\) and \(4\)
- Prime factorization:
- \(3 = 3\)
- \(4 = 2^2\)
- Combine the factors: \(2^2 \times 3 = 4 \times 3 = 12\)
- LCM: \(12\)

#### 5. \(10\) and \(23\)
- Prime factorization:
- \(10 = 2 \times 5\)
- \(23 = 23\)
- Combine the factors: \(2 \times 5 \times 23 = 230\)
- LCM: \(230\)

#### 6. \(2\) and \(4\)
- Prime factorization:
- \(2 = 2\)
- \(4 = 2^2\)
- Combine the factors: \(2^2 = 4\)
- LCM: \(4\)

#### 7. \(16\) and \(24\)
- Prime factorization:
- \(16 = 2^4\)
- \(24 = 2^3 \times 3\)
- Combine the factors: \(2^4 \times 3 = 16 \times 3 = 48\)
- LCM: \(48\)

#### 8. \(28\) and \(6\)
- Prime factorization:
- \(28 = 2^2 \times 7\)
- \(6 = 2 \times 3\)
- Combine the factors: \(2^2 \times 3 \times 7 = 4 \times 3 \times 7 = 84\)
- LCM: \(84\)

#### 9. \(10\) and \(19\)
- Prime factorization:
- \(10 = 2 \times 5\)
- \(19 = 19\)
- Combine the factors: \(2 \times 5 \times 19 = 190\)
- LCM: \(190\)

#### 10. \(14\) and \(28\)
- Prime factorization:
- \(14 = 2 \times 7\)
- \(28 = 2^2 \times 7\)
- Combine the factors: \(2^2 \times 7 = 4 \times 7 = 28\)
- LCM: \(28\)

#### 11. \(7\) and \(3\)
- Prime factorization:
- \(7 = 7\)
- \(3 = 3\)
- Combine the factors: \(7 \times 3 = 21\)
- LCM: \(21\)

#### 12. \(4\) and \(29\)
- Prime factorization:
- \(4 = 2^2\)
- \(29 = 29\)
- Combine the factors: \(2^2 \times 29 = 4 \times 29 = 116\)
- LCM: \(116\)

#### 13. \(19\) and \(9\)
- Prime factorization:
- \(19 = 19\)
- \(9 = 3^2\)
- Combine the factors: \(19 \times 3^2 = 19 \times 9 = 171\)
- LCM: \(171\)

#### 14. \(9\) and \(11\)
- Prime factorization:
- \(9 = 3^2\)
- \(11 = 11\)
- Combine the factors: \(3^2 \times 11 = 9 \times 11 = 99\)
- LCM: \(99\)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 44 \\
2. & 24 \\
3. & 24 \\
4. & 12 \\
5. & 230 \\
6. & 4 \\
7. & 48 \\
8. & 84 \\
9. & 190 \\
10. & 28 \\
11. & 21 \\
12. & 116 \\
13. & 171 \\
14. & 99 \\
\end{array}
}
\]