What is the LCM of 18 and 16?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 18 and 16. To find the LCM, we will identify the multiples of both numbers until we find the smallest common multiple.
Answer
The LCM of 18 and 16 is 144.
Answer for screen readers
The least common multiple (LCM) of 18 and 16 is 144.
Steps to Solve
- Find the prime factorization of each number
First, we need to factor both numbers into their prime factors.
For 18, we divide by the smallest primes:
$$ 18 = 2 \times 3^2 $$
For 16, it can be factored as:
$$ 16 = 2^4 $$
- Identify the highest powers of all prime factors
Next, we identify the highest power of each prime factor from both factorizations.
From the prime factorizations:
- For the prime factor $2$: the highest power is $2^4$ (from 16).
- For the prime factor $3$: the highest power is $3^2$ (from 18).
- Calculate the LCM using the highest powers
Now we can calculate the LCM by multiplying the highest powers found:
$$ LCM = 2^4 \times 3^2 $$
Calculating this gives:
$$ LCM = 16 \times 9 = 144 $$
The least common multiple (LCM) of 18 and 16 is 144.
More Information
The least common multiple (LCM) is the smallest number that is a multiple of each of the original numbers. Finding the LCM is particularly useful in adding or subtracting fractions with different denominators.
Tips
- A common mistake is to list the multiples and pick the wrong one as the smallest common multiple. Using prime factorization is a systematic way to ensure accuracy.
- Another mistake is forgetting to include all prime factors when calculating the LCM.
