What is the least common multiple (LCM) of 39 and 26?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 39 and 26. To solve this, we will find the multiples of each number and identify the smallest multiple they share.

Answer

$78$

Steps to Solve

Find the multiples of each number

The first step is to list some multiples of both 39 and 26.

Multiples of 39:

$39 \times 1 = 39$
$39 \times 2 = 78$
$39 \times 3 = 117$
$39 \times 4 = 156$
$39 \times 5 = 195$

Multiples of 26:

$26 \times 1 = 26$
$26 \times 2 = 52$
$26 \times 3 = 78$
$26 \times 4 = 104$
$26 \times 5 = 130$
$26 \times 6 = 156$

Identify common multiples

Now we check the multiples of both numbers to find the common multiples. From the lists above, we see:

The common multiples are 78 (from both) and 156.

Determine the least common multiple

To find the least common multiple, we take the smallest number from the common multiples.

The common multiples identified were 78 and 156, so the least common multiple is:

$$ \text{LCM}(39, 26) = 78 $$

The least common multiple of 39 and 26 is $78$.

More Information

The least common multiple (LCM) is the smallest positive integer that is divisible by both numbers. In this case, the LCM of 39 and 26, which is 78, can also be found using prime factorization or other methods, but listing multiples is often the simplest approach for small numbers.

Tips

Forgetting to check for all multiples, which could lead to missing the smallest common multiple. Always verify common multiples thoroughly.
Confusing the least common multiple with the greatest common divisor (GCD). Ensure you're looking for the smallest shared multiple, not the largest shared factor.

Thank you for voting!