LCM of 2, 5, and 4
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 2, 5, and 4. To solve this, we need to find the smallest positive integer that is divisible by all three numbers.
Answer
The LCM of 2, 5, and 4 is $20$.
Answer for screen readers
The least common multiple (LCM) of 2, 5, and 4 is $20$.
Steps to Solve
- Identify the prime factors of each number
Start by determining the prime factorization of each number:
- $2$ is a prime number, so its factorization is $2$.
- $5$ is also a prime number, so its factorization is $5$.
- $4$ can be factored into prime numbers as $2^2$.
- List all unique prime factors
Now we will list all the unique prime factors from the numbers we found:
- The unique prime factors are $2$ and $5$.
- Determine the highest power of each prime factor
Next, identify the highest power of each prime factor:
- For the prime factor $2$, the highest power in our numbers is $2^2$ (from number $4$).
- For the prime factor $5$, the highest power is $5^1$ (from number $5$).
- Multiply the highest powers of each prime factor
Finally, to calculate the least common multiple (LCM), multiply the highest powers of the unique prime factors together: $$ LCM = 2^2 \cdot 5^1 = 4 \cdot 5 = 20 $$
The least common multiple (LCM) of 2, 5, and 4 is $20$.
More Information
The least common multiple is useful in various mathematical contexts, including finding common denominators in fractions or solving problems that involve multiple cycles or periodic occurrences.
Tips
- Neglecting to consider all unique prime factors: Ensure all prime factors from every number are included.
- Using incorrect powers of prime factors: Always check that you are using the highest power of each prime factor.
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