LCM of 2 and 5
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 2 and 5. To find the LCM, we will identify the smallest number that is a multiple of both 2 and 5.
Answer
10
Answer for screen readers
The least common multiple (LCM) of 2 and 5 is 10
Steps to Solve
- List the prime factors of each number
Identify the prime factors of each number:
- For 2, the prime factor is 2.
- For 5, the prime factor is 5.
- Determine the highest power of each prime factor
The next step is to take the highest power of each prime factor appearing in the factorization of 2 and 5.
- Highest power of 2: $2^1$
- Highest power of 5: $5^1$
- Multiply these highest powers together
Now multiply these highest powers together to get the LCM:
$$ ext{LCM}(2, 5) = 2^1 \times 5^1 = 10$$
The least common multiple (LCM) of 2 and 5 is 10
More Information
The LCM is useful in problems involving adding, subtracting, or comparing fractions with different denominators. Fun fact: the LCM of any two prime numbers will always be their product!
Tips
A common mistake is to confuse the LCM with the greatest common divisor (GCD). Remember, the LCM of two numbers is the smallest number that both original numbers can divide into without leaving a remainder.
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