lcm of 25 and 45
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 25 and 45, which involves finding the smallest multiple that is evenly divisible by both numbers.
Answer
The LCM of 25 and 45 is $225$.
Answer for screen readers
The least common multiple (LCM) of 25 and 45 is $225$.
Steps to Solve
- Find the prime factorization of each number
To find the LCM, we first need to find the prime factorization of 25 and 45.
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The prime factorization of 25 is: $$ 25 = 5^2 $$
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The prime factorization of 45 is: $$ 45 = 3^2 \times 5^1 $$
- Identify the highest power of each prime
Next, we identify the highest power of each prime factor present in both factorizations.
- For the prime factor 3, the highest power is $3^2$ (from 45).
- For the prime factor 5, the highest power is $5^2$ (from 25).
- Multiply the highest powers together to find the LCM
Now, we multiply the highest powers of each prime to get the LCM: $$ \text{LCM} = 3^2 \times 5^2 $$ Calculating this, $$ \text{LCM} = 9 \times 25 = 225 $$
- Final Result with the LCM
Thus, the least common multiple (LCM) of 25 and 45 is $$ 225 $$
The least common multiple (LCM) of 25 and 45 is $225$.
More Information
The LCM is useful in various mathematical applications, such as finding common denominators in fractions or solving problems involving synchronization of cycles, like schedules.
Tips
- Confusing LCM with GCD (greatest common divisor) is common. Always ensure you are practicing LCM specifically to avoid this mix-up.
- Forgetting to consider all prime factors is another error. Make sure to include each prime factor, raising it to the highest power present in the factorizations.
