lcm 35 and 50
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 35 and 50. To solve this, we can find the prime factorization of both numbers and then determine the LCM based on those factors.
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
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Find the prime factorization of 35
To find the prime factors of 35, we can divide by the smallest prime number.
$$ 35 = 5 \times 7 $$ -
Find the prime factorization of 50
Now, we find the prime factors of 50.
$$ 50 = 2 \times 5^2 $$ -
List the unique prime factors
Next, we will list all unique prime factors from both factorizations:
The prime factors are: $2$, $5$, and $7$. -
Determine the highest powers of each factor
For each unique prime factor, we take the highest power that appears in the factorizations:
- For $2$: The highest power is $2^1$ from 50.
- For $5$: The highest power is $5^2$ from 50.
- For $7$: The highest power is $7^1$ from 35.
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Calculate the LCM
Now we multiply these highest powers together to get the LCM:
$$ \text{LCM} = 2^1 \times 5^2 \times 7^1 $$
Calculating this gives:
$$ \text{LCM} = 2 \times 25 \times 7 $$ $$ = 350 $$
The least common multiple (LCM) of 35 and 50 is 350.
More Information
The least common multiple is significant in various mathematical applications, such as finding common denominators or solving problems involving periodic events. The LCM helps us understand how often two or more numbers coincide.
Tips
- Forgetting to consider all prime factors: Some might only consider the factors that are common instead of listing all unique prime factors.
- Incorrectly calculating the highest powers: Make sure to review the prime factorization carefully to avoid miscalculating the powers.
