LCM of 35 and 10
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 35 and 10. To solve this, we can use the prime factorization method or the formula that involves the greatest common divisor (GCD).
Answer
$70$
Answer for screen readers
The least common multiple of 35 and 10 is $70$.
Steps to Solve
- Find the prime factorization of each number
For 35:
- The prime factors are 5 and 7, so we write it as: $$ 35 = 5^1 \times 7^1 $$
For 10:
- The prime factors are 2 and 5, so we write it as: $$ 10 = 2^1 \times 5^1 $$
- Determine the highest power of each prime factor
For the prime factors found:
- Prime factor 2: Highest power is (2^1) (from 10)
- Prime factor 5: Highest power is (5^1) (common in both)
- Prime factor 7: Highest power is (7^1) (from 35)
- Multiply the highest powers of all prime factors
Now, we multiply these together to find the LCM: $$ \text{LCM} = 2^1 \times 5^1 \times 7^1 $$
Calculating it: $$ \text{LCM} = 2 \times 5 \times 7 $$
Continuing with the multiplication: $$ 2 \times 5 = 10 $$ $$ 10 \times 7 = 70 $$
- Final Result
Therefore, the least common multiple of 35 and 10 is: $$ \text{LCM} = 70 $$
The least common multiple of 35 and 10 is $70$.
More Information
The least common multiple (LCM) is useful in many mathematical applications, particularly when dealing with fractions, time intervals, and solving problems involving multiple cycles or periods.
Tips
- Mixing up LCM with GCD: Ensure to focus on finding the least common multiple instead of the greatest common divisor.
- Incorrectly calculating the powers of prime factors: Double-check the factorization to prevent errors.
