LCM of 35 and 50
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 35 and 50. To find the LCM, we can use the prime factorization of both numbers and then determine the highest powers of each prime factor appearing in the factorization.
Answer
The LCM of \(35\) and \(50\) is \(350\).
Answer for screen readers
The least common multiple (LCM) of 35 and 50 is (350).
Steps to Solve
- Prime Factorization of 35
Start by finding the prime factors of 35.
$$ 35 = 5^1 \times 7^1 $$
- Prime Factorization of 50
Next, find the prime factors of 50.
$$ 50 = 2^1 \times 5^2 $$
- Identify the Highest Powers of Each Prime Factor
Now, list all the unique prime factors from both numbers and take the highest power for each prime.
- For the prime factor (2): The highest power is (2^1) (from 50).
- For the prime factor (5): The highest power is (5^2) (from 50).
- For the prime factor (7): The highest power is (7^1) (from 35).
- Calculate the LCM
Now, multiply the highest powers of all prime factors together to find the LCM.
$$ LCM = 2^1 \times 5^2 \times 7^1 $$
Calculating it gives:
$$ LCM = 2 \times 25 \times 7 $$
- Final Calculation
Now perform the final multiplication.
$$ 2 \times 25 = 50 $$
Then,
$$ 50 \times 7 = 350 $$
So, the LCM of 35 and 50 is 350.
The least common multiple (LCM) of 35 and 50 is (350).
More Information
The least common multiple (LCM) is useful in various applications, including adding and subtracting fractions with different denominators, and finding synchronization points of repeating events. The LCM of two numbers is the smallest number that is a multiple of both.
Tips
- Forgetting to take the highest power of each prime factor can lead to an incorrect LCM.
- Not listing all unique prime factors from both numbers can also result in missing factors.
