What is the least common multiple of 10 and 8?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 10 and 8. To find the LCM, we will identify the multiples of both numbers and determine the smallest multiple that they share.
Answer
40
Answer for screen readers
The final answer is 40
Steps to Solve
- Find the Prime Factors
Break down each number into its prime factors.
For 10: $10 = 2 imes 5$
For 8: $8 = 2^3$
- Identify the Highest Power of Each Prime Number
List all prime numbers found and use the highest power of each prime number.
Prime numbers: 2 and 5
Highest powers: $2^3$ and $5^1$
- Calculate the LCM
Multiply the highest powers of all prime numbers together to find the LCM.
$$LCM = 2^3 imes 5^1 = 8 imes 5 = 40$$
The final answer is 40
More Information
The LCM is helpful in solving problems that involve adding, subtracting, or comparing fractions with different denominators.
Tips
A common mistake when finding the LCM is to miss one of the prime numbers or not use the highest power of a prime. Always double-check the prime factorization and the highest powers.
