What is the least common multiple of 10 and 9?

Understand the Problem

The question is asking for the least common multiple (LCM) of the numbers 10 and 9. To find the LCM, we typically determine the multiples of each number and identify the smallest multiple that both numbers share.

Answer

The least common multiple of 10 and 9 is $90$.

Steps to Solve

List the multiples of each number

Start by listing the first several multiples of each number.

For 10:

$10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...$

For 9:

$9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ...$

Identify the common multiples

Now, look for the common multiples from the lists generated above.

From the lists:

The multiples of 10 are: $10, 20, 30, 40, 50, 60, 70, 80, 90, ...$
The multiples of 9 are: $9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...$

Common multiples found: $90, ...$

Determine the least common multiple

The smallest number that appears in both lists is the least common multiple.

Thus, the LCM of 10 and 9 is:

$$ LCM(10, 9) = 90 $$

The least common multiple of 10 and 9 is $90$.

More Information

The least common multiple (LCM) is useful in various mathematical applications, including adding fractions and finding common denominators. It's the smallest number that is a multiple of both numbers.

Tips

Failing to list enough multiples: Always ensure to list sufficient multiples to find common ones.
Confusing LCM with greatest common factor (GCF): Remember that LCM is the smallest shared multiple, whereas GCF is the largest shared factor.

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