LCM of 3 and 13
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 3 and 13. To find the LCM, you typically can list the multiples of each number or use the prime factorization method. Since both numbers are prime, the LCM will be their product.
Answer
The least common multiple of 3 and 13 is $39$.
Answer for screen readers
The least common multiple of 3 and 13 is $39$.
Steps to Solve
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Identify the two numbers
We are looking for the least common multiple of the numbers 3 and 13. -
Determine the prime factors
Both 3 and 13 are prime numbers, meaning their only factors are 1 and themselves.
- The prime factors of 3 are: $3$
- The prime factors of 13 are: $13$
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Calculate the LCM
Since the numbers are prime, the least common multiple is simply the product of the two numbers:
$$ \text{LCM}(3, 13) = 3 \times 13 $$ -
Find the product
Now, calculate the product:
$$ \text{LCM}(3, 13) = 39 $$
The least common multiple of 3 and 13 is $39$.
More Information
The least common multiple (LCM) is the smallest number that is a multiple of both numbers. Since both numbers are prime, the LCM is computed by multiplying them together. Fun fact: The LCM is useful in problems involving fractions, where a common denominator is needed.
Tips
- Confusing LCM with GCD (greatest common divisor); remember, LCM is about finding the smallest multiple that both numbers share, whereas GCD is the largest number that divides both numbers.
- Forgetting that the product of two prime numbers is their LCM when they have no common factors.
