The first common multiple of 4 and 8 is 8.
Understanding Common Multiples
A **common multiple** of two or more numbers is a number that is a multiple of all of them. The *first* common multiple is also known as the **Least Common Multiple (LCM)**. It is the smallest positive number that is a multiple of all the given numbers.To find the first common multiple, we can list the multiples of each number and identify the smallest number that appears in both lists.
Multiples of 4:
The multiples of 4 are found by multiplying 4 by consecutive positive integers: * 4 × 1 = 4 * 4 × 2 = 8 * 4 × 3 = 12 * 4 × 4 = 16 * 4 × 5 = 20 * 4 × 6 = 24 * 4 × 7 = 28 * 4 × 8 = 32 * 4 × 9 = 36 * 4 × 10 = 40 ...and so on.Multiples of 8:
The multiples of 8 are found by multiplying 8 by consecutive positive integers: * 8 × 1 = 8 * 8 × 2 = 16 * 8 × 3 = 24 * 8 × 4 = 32 * 8 × 5 = 40 ...and so on.Identifying the First Common Multiple
By comparing the lists of multiples for 4 and 8, we can identify the numbers that appear in both:| Multiples of 4 | Multiples of 8 | Common Multiples |
|---|---|---|
| 4 | ||
| 8 | 8 | 8 |
| 12 | ||
| 16 | 16 | 16 |
| 20 | ||
| 24 | 24 | 24 |
| 28 | ||
| 32 | 32 | 32 |
| 36 | ||
| 40 | 40 | 40 |
From the table, it is clear that the common multiples of 4 and 8 are 8, 16, 24, 32, and 40, among others. The smallest number in this list of common multiples is 8. This confirms that the first common multiple of 4 and 8 is 8.
