lcm of 25 and 16

Steps to Solve

1. 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:
$$ 16 = 2^4 $$

2. 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:

$$ LCM = 2^4 \cdot 5^2 $$

3. 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:
$$ LCM = 16 \cdot 25 $$

4. Final multiplication

Finally, we perform the multiplication:
$$ 16 \cdot 25 = 400 $$

Thus, the least common multiple of 25 and 16 is 400.