lcm of 25 and 16
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 25 and 16. To find the LCM, we need to determine the smallest multiple that is divisible by both numbers.
Answer
The least common multiple (LCM) of 25 and 16 is $400$.
Answer for screen readers
The least common multiple (LCM) of 25 and 16 is $400$.
Steps to Solve
- Identify the prime factors of each number
First, we need to find the prime factors of both numbers.
For 25:
$$ 25 = 5^2 $$
For 16:
$$ 16 = 2^4 $$
- Combine the highest powers of all prime factors
Next, we take each prime factor found and use the highest power that appears in the factorizations.
- From 25, we have $5^2$.
- From 16, we have $2^4$.
Thus, we will combine these:
$$ LCM = 2^4 \cdot 5^2 $$
- Calculate the LCM
Now, we need to compute the value of the LCM from the combined factors:
First, calculate $2^4$:
$$ 2^4 = 16 $$
Then, calculate $5^2$:
$$ 5^2 = 25 $$
Now multiply the two results:
$$ LCM = 16 \cdot 25 $$
- Final multiplication
Finally, we perform the multiplication:
$$ 16 \cdot 25 = 400 $$
Thus, the least common multiple of 25 and 16 is 400.
The least common multiple (LCM) of 25 and 16 is $400$.
More Information
The least common multiple is significant in various applications, especially in solving problems involving fractions and finding common denominators. It represents the smallest number into which both original numbers can evenly divide.
Tips
- Forgetting to find the prime factorization of the numbers.
To avoid this, always write down the factors clearly before combining them. - Miscalculating the multiplication when finding the LCM.
Double-check your calculations to ensure accuracy.