What is the LCM of 50 and 35?
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 50 and 35. To find the LCM, we can use the prime factorization method or the formula that states LCM(a, b) = (a * b) / GCD(a, b), where GCD is the greatest common divisor.
Answer
The LCM of 50 and 35 is $350$.
Answer for screen readers
The least common multiple (LCM) of 50 and 35 is $350$.
Steps to Solve
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Identify the numbers We need to find the LCM of the numbers 50 and 35.
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Find the prime factorization of each number
- For 50:
- $50 = 2 \times 5^2$
- For 35:
- $35 = 5 \times 7$
- For 50:
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List all prime factors We take the highest power of each prime factor from both factorizations:
- The prime factor 2 appears in 50: $2^1$
- The prime factor 5 appears in both: $5^2$ (from 50)
- The prime factor 7 appears in 35: $7^1$
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Compute the LCM Multiply the highest powers of all the primes together: $$ \text{LCM} = 2^1 \times 5^2 \times 7^1 $$
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Calculate the LCM Perform the multiplications:
- First calculate $5^2 = 25$.
- Then calculate $2 \times 25 = 50$.
- Finally, calculate $50 \times 7 = 350$.
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Result The LCM of 50 and 35 is 350.
The least common multiple (LCM) of 50 and 35 is $350$.
More Information
The least common multiple is useful for finding common denominators in fractions or when combining cycles in problems related to time and scheduling.
Tips
Common mistakes include:
- Forgetting to include all prime factors when combining.
- Failing to take the highest power of each prime factor.
- Confusing LCM with GCD, leading to incorrect calculations.
