To find the common multiples of 3 and 6 that are less than 20, we need to identify numbers between 1 and 19 that are divisible by both 3 and 6. Here is a step-by-step explanation:
1. Identify the Range: We are considering the numbers between 1 and 19 (inclusive).
2. Understand the Multiples:
- A multiple of a number is the product of that number and any integer.
- We need to find numbers that are multiples of both 3 and 6 in the given range.
3. Common Multiples of 3 and 6:
- A number that is a common multiple of 3 and 6 must be divisible by their least common multiple (LCM). The LCM of 3 and 6 is 6.
- Therefore, we will focus on multiples of 6 within the range of 1 to 19.
4. Finding the Multiples:
- Start from the smallest multiple of 6 which is 6 itself, then keep adding 6 until we reach a number that exceeds 19.
- The multiples of 6 within this range are:
- 6 (since 6 1 = 6)
- 12 (since 6 2 = 12)
- 18 (since 6 * 3 = 18)
5. Form the List: The common multiples of 3 and 6 that are less than 20 are:
- 6, 12, and 18
Hence, the common multiples of 3 and 6 that are less than 20 are: 6, 12, and 18.
