lcm 9 15
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 9 and 15, which is the smallest number that is a multiple of both 9 and 15.
Answer
The least common multiple (LCM) of 9 and 15 is $45$.
Answer for screen readers
The least common multiple (LCM) of 9 and 15 is $45$.
Steps to Solve
- Find the prime factorization of each number
To find the LCM, we first need the prime factorization of both numbers. For 9, the prime factorization is: $$ 9 = 3^2 $$
For 15, the prime factorization is: $$ 15 = 3^1 \times 5^1 $$
- Identify the highest power of each prime factor
Next, we identify the highest exponent for each prime factor used in the factorizations. Here, we have the prime factors 3 and 5.
- The highest power of 3 is $3^2$ (from 9).
- The highest power of 5 is $5^1$ (from 15).
- Multiply the highest powers of the prime factors
Now, we calculate the LCM by multiplying these highest powers together. $$ LCM = 3^2 \times 5^1 $$
- Calculate the LCM
Finally, we perform the multiplication: $$ LCM = 9 \times 5 = 45 $$
The least common multiple (LCM) of 9 and 15 is $45$.
More Information
The least common multiple (LCM) is useful in various fields of math and applied sciences, especially in problems involving fractions, scheduling, or finding common periods in cycles. The LCM is the smallest number into which both original numbers can divide evenly.
Tips
- Forgetting to include all prime factors when determining the highest powers can lead to incorrect calculations.
- Multiplying the prime factors incorrectly; ensure to carefully multiply the highest powers.
