lcm of 13 and 4
Understand the Problem
The question is asking for the least common multiple (LCM) of the two numbers, 13 and 4. To find this, we need to identify the smallest positive integer that is divisible by both numbers.
Answer
The least common multiple of 13 and 4 is $52$.
Answer for screen readers
The least common multiple (LCM) of 13 and 4 is 52.
Steps to Solve
- Identify the prime factors of each number
For the numbers 13 and 4, we first find their prime factors.
- The prime factorization of 13 is simply $13$ (since 13 is a prime number).
- The prime factorization of 4 is $2^2$ (since $4 = 2 \times 2$).
- List the highest powers of each prime factor
Next, we need to find the highest powers of each prime factor from both numbers.
- The prime factors we have are 13 and 2.
- The highest power of 13 is $13^1$.
- The highest power of 2 is $2^2$.
- Multiply the highest powers of the prime factors
Now we can find the LCM by multiplying these highest powers together:
$$ \text{LCM} = 13^1 \times 2^2 $$
Calculating this gives:
$$ \text{LCM} = 13 \times 4 = 52 $$
The least common multiple (LCM) of 13 and 4 is 52.
More Information
The least common multiple (LCM) is particularly useful in problems involving fractions or ratios, where finding a common denominator is necessary. In this case, the LCM of 13 and 4, which is 52, represents the smallest number that both numbers can divide without leaving a remainder.
Tips
- Forgetting Prime Factorization: Some may skip the step of finding prime factors, which can lead to errors in determining the LCM.
- Incorrect Multiplication: Be cautious during multiplication of the prime factors; double-check your calculations to avoid mistakes.
