Find the LCM of Denominators: 9 and 6 Problem

Q: Why isn't the answer just 9 × 6 = 54?

That would give you a common multiple, but not the least common multiple! $9 \times 6 = 54$ works, but $18$ is smaller and still works for both numbers.

Q: How do I know when to stop listing multiples?

Stop as soon as you find the first number that appears in both lists. In this case, $18$ appears in both the multiples of 9 and multiples of 6, so that's your LCM!

Q: Can I use prime factorization instead?

Yes! $9 = 3^2$ and $6 = 2 \times 3$, so LCM = $2 \times 3^2 = 18$. Both methods give the same answer.

LCM with Listing Multiples Method

You have a pair of denominators, what is their least common multiple?

$\boxed 9~~~\boxed 6$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

You have a pair of denominators, what is their least common multiple?

$\boxed 9~~~\boxed 6$

Step-by-step solution

To find the least common multiple (LCM) of $9$ and $6$ , list the multiples of each number until the smallest common multiple appears.

Multiples of $9$ : $9, 18, 27, 36, \ldots$

Multiples of $6$ : $6, 12, 18, 24, 30, \ldots$

The smallest common multiple is $18$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: LCM is the smallest positive number divisible by both numbers
Technique: List multiples until first common multiple appears: 9, 18 and 6, 12, 18
Check: Verify 18 ÷ 9 = 2 and 18 ÷ 6 = 3 (both whole numbers) ✓

Common Mistakes

Avoid these frequent errors

Confusing LCM with GCF
Don't find the greatest common factor (GCF = 3) instead of LCM = wrong answer of 3! LCM finds the smallest shared multiple, while GCF finds the largest shared factor. Always look for the first number that appears in both multiplication tables.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

Why isn't the answer just 9 × 6 = 54?

That would give you a common multiple, but not the least common multiple! $9 \times 6 = 54$ works, but $18$ is smaller and still works for both numbers.

How do I know when to stop listing multiples?

Stop as soon as you find the first number that appears in both lists. In this case, $18$ appears in both the multiples of 9 and multiples of 6, so that's your LCM!

Can I use prime factorization instead?

Yes! $9 = 3^2$ and $6 = 2 \times 3$ , so LCM = $2 \times 3^2 = 18$ . Both methods give the same answer.

What if the numbers don't share any common factors?

If two numbers have no common factors (like 4 and 9), then their LCM is simply their product. For example, LCM of 4 and 9 would be $4 \times 9 = 36$ .

Why is finding LCM important for fractions?

When adding or subtracting fractions with different denominators, you need a common denominator. The LCM gives you the smallest common denominator, making calculations easier!

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