lcm of 16 and 15
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 16 and 15. To solve this, we will consider the prime factors of both numbers and calculate the LCM using those factors.
Answer
$240$
Answer for screen readers
The least common multiple of 16 and 15 is $240$.
Steps to Solve
- Prime Factorization of Each Number
First, we need to find the prime factors of each number.
For 16, the prime factorization is: $$ 16 = 2^4 $$
For 15, the prime factorization is: $$ 15 = 3^1 \times 5^1 $$
- Identify the Highest Powers of Each Prime
Next, we will identify the highest powers of all prime factors involved in both numbers.
The prime factors are 2, 3, and 5.
- The highest power of 2: $2^4$ (from 16)
- The highest power of 3: $3^1$ (from 15)
- The highest power of 5: $5^1$ (from 15)
- Multiply the Highest Powers Together
Now we multiply the highest powers identified to find the LCM:
$$ LCM = 2^4 \times 3^1 \times 5^1 $$
Calculating this:
$$ LCM = 16 \times 3 \times 5 $$
- Perform the Multiplication
Calculating step by step:
First, multiply 16 and 3:
$$ 16 \times 3 = 48 $$
Next, multiply the result by 5:
$$ 48 \times 5 = 240 $$
Thus, the least common multiple is: $$ LCM = 240 $$
The least common multiple of 16 and 15 is $240$.
More Information
The least common multiple (LCM) is the smallest positive integer that is divisible by both numbers. The LCM is often used in problems involving fractions and finding common denominators.
Tips
- Forgetting to include all prime factors: When calculating the LCM, ensure that you include all prime factors, even if one number does not contain that prime number.
- Not using the highest powers of each prime: Always take the highest power of each prime factor when finding the LCM.
