What is the LCM of 3, 5, and 7?
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 3, 5, and 7. To solve this, we will identify the multiples of each number and determine the smallest multiple that is common to all three.
Answer
$105$
Answer for screen readers
The least common multiple of 3, 5, and 7 is $105$.
Steps to Solve
- List the multiples of each number
First, let's identify the multiples of the numbers 3, 5, and 7.
-
Multiples of 3:
$3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, ...$ -
Multiples of 5:
$5, 10, 15, 20, 25, 30, 35, 40, 45, ...$ -
Multiples of 7:
$7, 14, 21, 28, 35, 42, 49, 56, 63, ...$
- Identify common multiples
Next, we look for numbers that appear in all three lists of multiples. The common multiples we can find are:
- Common multiples:
$15, 30, 45, 60, ...$
- Find the least common multiple
From the common multiples, the smallest one is the least common multiple (LCM).
Thus, we find that:
$$ \text{LCM}(3, 5, 7) = 105 $$
The least common multiple of 3, 5, and 7 is $105$.
More Information
The least common multiple (LCM) is particularly useful in problems involving fractions, such as finding a common denominator, and in scheduling tasks that repeat at different intervals.
Tips
- A common mistake is to stop at the first common multiple found instead of looking for the smallest. Always ensure you're identifying the least common multiple by checking all options.
- Confusing LCM with the greatest common divisor (GCD) can also mislead. Remember that LCM is the smallest shared multiple, while GCD is the largest shared factor.
