Find the LCM of Denominators: Calculating LCM(6,8)

Q: Why can't I just multiply 6 and 8 to get the LCM?

Multiplying gives you a common multiple (48), but not the least common multiple! The LCM of 6 and 8 is actually 24, which is smaller than 48.

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

Stop as soon as you find the first number that appears in both lists. That's your LCM! You don't need to keep going once you find the match.

Q: Is there a faster way than listing all the multiples?

Yes! You can use prime factorization or the formula LCM(a,b) = (a × b) ÷ GCF(a,b). But listing multiples is often clearer for smaller numbers.

Least Common Multiples with Listing Method

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

$\boxed 6~~~\boxed 8$

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Step-by-step written solution

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Understand the problem

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

$\boxed 6~~~\boxed 8$

Step-by-step solution

To find the least common multiple (LCM) of $6$ and $8$ , list the multiples of each number until the smallest common multiple appears.

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

Multiples of $8$ : $8, 16, 24, 32, 40, \ldots$

The smallest common multiple is $24$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: LCM is the smallest positive number divisible by both
Technique: List multiples of each: 6, 12, 18, 24... and 8, 16, 24...
Check: Confirm 24 ÷ 6 = 4 and 24 ÷ 8 = 3 ✓

Common Mistakes

Avoid these frequent errors

Confusing LCM with GCF or multiplying the numbers together
Don't just multiply 6 × 8 = 48! This gives you a common multiple but not the smallest one. Always find the actual smallest common multiple by listing or using prime factorization.

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 can't I just multiply 6 and 8 to get the LCM?

Multiplying gives you a common multiple (48), but not the least common multiple! The LCM of 6 and 8 is actually 24, which is smaller than 48.

How do I know when to stop listing multiples?

Stop as soon as you find the first number that appears in both lists. That's your LCM! You don't need to keep going once you find the match.

Is there a faster way than listing all the multiples?

Yes! You can use prime factorization or the formula LCM(a,b) = (a × b) ÷ GCF(a,b). But listing multiples is often clearer for smaller numbers.

What if one number divides evenly into the other?

Great question! If one number is a multiple of the other, then the larger number is the LCM. For example, LCM(4, 12) = 12 since 12 ÷ 4 = 3.

Do I always get the same answer with different methods?

Absolutely! Whether you list multiples, use prime factorization, or apply formulas, the LCM is always unique. There's only one least common multiple for any pair of numbers.

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