What is the LCM of 14 and 42?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 14 and 42. We will find the LCM by determining the smallest number that is a multiple of both 14 and 42.
Answer
The least common multiple of 14 and 42 is $42$.
Answer for screen readers
The least common multiple of 14 and 42 is $42$.
Steps to Solve
- Identify the multiples of both numbers
To find the LCM, we first identify the multiples of both 14 and 42.
-
Multiples of 14: $$ 14, 28, 42, 56, 70, 84, ... $$
-
Multiples of 42: $$ 42, 84, 126, ... $$
- Find the smallest common multiple
Next, we look for the smallest number that appears in both lists of multiples.
From the multiples we listed, the number 42 appears in both lists, but we keep checking for smaller common values. The next potential multiple from both lists is 84, but it exceeds 42.
- Determine the least common multiple (LCM)
Since the smallest common multiple of both 14 and 42 is 42, we can conclude that: $$ \text{LCM}(14, 42) = 42 $$
The least common multiple of 14 and 42 is $42$.
More Information
The LCM is useful in various mathematical applications, such as solving problems involving fractions, where a common denominator is required. The number 42 is not only a common multiple of 14 and 42, but is also interesting as a triangular number.
Tips
- A common mistake is to stop at the first multiple of either number without checking both lists. Make sure to compare multiples carefully to find the smallest common one.
AI-generated content may contain errors. Please verify critical information
