List all 2-digit multiples of 27
The Correct Answer and Explanation is:
To list all 2-digit multiples of 27, we start by identifying the first and last two-digit numbers that are divisible by 27.
Step 1: Identify the first 2-digit multiple of 27
We begin by dividing the smallest two-digit number, 10, by 27:
[
\frac{10}{27} \approx 0.37
]
This result means that 27 does not divide evenly into 10. To find the smallest two-digit multiple, we calculate the first multiple of 27 that exceeds 10. Dividing 10 by 27, we round up to the next whole number, which is 1, and then multiply by 27:
[
27 \times 1 = 27
]
Thus, 27 is the first two-digit multiple of 27.
Step 2: Identify the last 2-digit multiple of 27
Next, we find the largest two-digit number divisible by 27. We begin by dividing the largest two-digit number, 99, by 27:
[
\frac{99}{27} \approx 3.67
]
Since we need a whole number, we round down to 3. Multiplying by 27 gives:
[
27 \times 3 = 81
]
Thus, 81 is the largest two-digit multiple of 27.
Step 3: List all 2-digit multiples of 27
We now know that the two-digit multiples of 27 range from 27 to 81. These multiples are:
[
27, 54, 81
]
These are the only two-digit multiples of 27.
Explanation:
Multiples of any number can be found by multiplying that number by whole numbers. For 27, multiplying by 1, 2, and 3 yields the two-digit multiples: 27, 54, and 81. Any multiple of 27 greater than 81 would result in a three-digit number (i.e., 27 × 4 = 108), and any smaller multiple would fall outside the two-digit range. Hence, the complete list of two-digit multiples of 27 is 27, 54, and 81.