lcm of 16 and 25

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 16 and 25. To find this, we need to identify the multiples of both numbers and find the smallest one that they share. Alternatively, LCM can also be calculated using the formula LCM(a, b) = (a * b) / GCD(a, b), where GCD is the greatest common divisor.

Answer

The LCM of 16 and 25 is $400$.

Steps to Solve

Identify the numbers We want to find the least common multiple (LCM) of the numbers 16 and 25.
Calculate the GCD (Greatest Common Divisor) Since 16 and 25 are both powers of distinct primes (16 is $2^4$ and 25 is $5^2$), we can say that their GCD is 1 because they have no common factors.
Use the LCM Formula Now we can use the formula for LCM:

$$ \text{LCM}(a, b) = \frac{a \cdot b}{\text{GCD}(a, b)} $$

Substituting in our values,

$$ \text{LCM}(16, 25) = \frac{16 \cdot 25}{1} $$

Perform the multiplication Calculate the multiplication in the equation:

$$ 16 \cdot 25 = 400 $$

So we have:

$$ \text{LCM}(16, 25) = 400 $$

The least common multiple of 16 and 25 is 400.

More Information

The least common multiple is the smallest number that is a multiple of both numbers. In this case, 400 is the smallest number that can be evenly divided by both 16 and 25. This method using GCD can be more efficient than listing out all the multiples, especially for large numbers.

Tips

Forgetting to calculate the GCD: Ensure you understand that the GCD is important for using the LCM formula.
Incorrect multiplication: When performing $16 \times 25$, some may miscalculate the product as 350 instead of 400. Double-checking multiplication can prevent this.

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