LCM of 7 and 18
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 7 and 18, which is a standard mathematical concept used to find the smallest multiple that is common to two or more numbers.
Answer
$126$
Answer for screen readers
The least common multiple (LCM) of 7 and 18 is $126$.
Steps to Solve
-
Identify the prime factorization of each number
The first step is to break down the numbers into their prime factors.
- For 7, the prime factorization is simply $7$ (since it is a prime number).
- For 18, the factorization is $2 \times 3^2$.
-
List all prime factors with the highest powers
Next, we take each prime factor found in either number and use the highest power of each.
- From 7, we take $7^1$.
- From 18, we take $2^1$ and $3^2$.
-
Multiply the highest powers of all prime factors
Now, we multiply these highest powers together to find the LCM. $$ LCM = 2^1 \times 3^2 \times 7^1 $$
This translates to: $$ LCM = 2 \times 9 \times 7 $$
-
Calculate the final product
Finally, we calculate this product step-by-step:
- First, calculate $2 \times 9 = 18$.
- Then, multiply $18 \times 7 = 126$.
The least common multiple (LCM) of 7 and 18 is $126$.
More Information
The LCM is used in various fields, such as in solving problems involving fractions with different denominators, and in scheduling events that repeat at different intervals. Finding the LCM helps in simplifying such processes.
Tips
- Confusing GCD with LCM: Some might confuse the greatest common divisor (GCD) with the least common multiple (LCM). Remember that LCM finds a common multiple, while GCD finds a common divisor.
- Not using prime factorization: Skipping the prime factorization step can lead to mistakes. Ensure that each number is factored correctly to avoid errors.
