What is the lowest common multiple of 26 and 39?
Understand the Problem
The question is asking to find the lowest common multiple (LCM) of the numbers 26 and 39. The LCM is the smallest number that is a multiple of both numbers. To find it, we can list the multiples of each number or use the formula involving their greatest common divisor (GCD).
Answer
The lowest common multiple of 26 and 39 is $78$.
Answer for screen readers
The lowest common multiple of 26 and 39 is $78$.
Steps to Solve
- Find the prime factors of each number
First, we need to find the prime factors of 26 and 39.
- The prime factorization of 26 is: $$ 26 = 2 \times 13 $$
- The prime factorization of 39 is: $$ 39 = 3 \times 13 $$
- Identify the highest power of each prime factor
Next, for the LCM, we take the highest power of each prime factor present in either number.
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From 26, we have the prime factors:
- $2^1$
- $13^1$
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From 39, we have the prime factors:
- $3^1$
- $13^1$
Now we take the highest powers:
- $2^1$ from 26
- $3^1$ from 39
- $13^1$ from both
- Calculate the LCM
Now we can find the LCM by multiplying these highest powers together: $$ LCM(26, 39) = 2^1 \times 3^1 \times 13^1 $$
Calculating it: $$ LCM(26, 39) = 2 \times 3 \times 13 = 78 $$
The lowest common multiple of 26 and 39 is $78$.
More Information
The LCM is used in various mathematical applications, such as adding or subtracting fractions with different denominators. Knowing how to find the LCM can also help in simplifying problems involving time, work, or periodic events.
Tips
- Forgetting to consider the highest powers of prime factors.
- Miscalculating the prime factorization of the numbers. Be careful to ensure all factors are correct.
