What is the LCM of 25 and 4?
Understand the Problem
The question is asking for the least common multiple (LCM) of the two numbers 25 and 4. To find the LCM, we can list the multiples of each number and identify the smallest multiple they have in common, or use the prime factorization method.
Answer
$100$
Answer for screen readers
The least common multiple (LCM) of 25 and 4 is $100$.
Steps to Solve
- List the multiples of each number We start by listing out the multiples for both numbers.
For 25:
$25, 50, 75, 100, 125, 150, 175, 200, \ldots$
For 4:
$4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, \ldots$
- Identify the least common multiple Next, we look for the smallest number that appears in both lists of multiples. From the lists, the common multiples are 100, 200, and so on. The smallest one is:
$$ \text{LCM} = 100 $$
- Using prime factorization (optional) We can also find the LCM using prime factorization. The prime factorization of each number is:
- $25 = 5^2$
- $4 = 2^2$
To find the LCM, take the highest power of each prime that appears:
- The highest power of 5 is $5^2$
- The highest power of 2 is $2^2$
Thus, we calculate:
$$ \text{LCM} = 5^2 \times 2^2 = 25 \times 4 = 100 $$
The least common multiple (LCM) of 25 and 4 is $100$.
More Information
The least common multiple is the smallest number that is a multiple of both integers. Finding the LCM can be useful in problems involving synchronization of events, such as finding common time frames for repeating schedules.
Tips
- Not listing enough multiples to find the LCM; ensure you list enough terms to identify the smallest common multiple.
- Confusing LCM with GCD (Greatest Common Divisor); remember that LCM is about the smallest common multiple.
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