What is the least common multiple of 9 and 8?
Understand the Problem
The question is asking to find the least common multiple (LCM) of the numbers 9 and 8. To do this, we will determine the multiples of each number and identify the smallest multiple that they both share.
Answer
72
Answer for screen readers
The least common multiple (LCM) of 9 and 8 is 72
Steps to Solve
- Find the prime factors of each number
To find the LCM, first find the prime factorization of each number. Prime factors of 9: $9 = 3 \times 3 = 3^2$ Prime factors of 8: $8 = 2 \times 2 \times 2 = 2^3$
- Identify the highest power of each prime factor
For LCM, take the highest power of each prime number present in the factorizations.
Highest power of 2: $2^3$ Highest power of 3: $3^2$
- Calculate the LCM by multiplying these highest powers together
$$LCM = 2^3 \times 3^2$$ Calculating this: $$2^3 = 8$$ $$3^2 = 9$$ $$LCM = 8 \times 9 = 72$$
The least common multiple (LCM) of 9 and 8 is 72
More Information
LCM is a useful concept for solving problems involving adding or subtracting fractions with different denominators, scheduling, and more.
Tips
A common mistake is not taking the highest power of all prime factors. Ensure you use the highest power of each prime factor from any of the numbers.
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