Find the LCM: Calculating Least Common Multiple of 8 and 12

Q: Is the LCM always bigger than both original numbers?

Usually yes! The LCM is typically larger than both numbers, like how 24 is bigger than both 8 and 12. The only exception is when one number divides evenly into the other.

Q: What if I can't find a common multiple quickly?

Keep listing! Write out at least 5-6 multiples of each number. The LCM of small numbers like 8 and 12 will appear within the first few multiples.

Q: Can I use prime factorization instead?

Yes! Factor both numbers: $ 8 = 2^3 $ and $ 12 = 2^2 \times 3 $. Take the highest power of each prime: $ 2^3 \times 3 = 24 $.

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

Stop when you find the first number that appears in both lists. That's your LCM! Don't keep going once you've found the common multiple.

Q: What's the difference between LCM and GCF?

LCM finds the smallest multiple both numbers share, while GCF finds the largest factor both numbers share. LCM is usually bigger than your original numbers!

LCM with Multiple Listing Method

Determine the least common multiple of 8 and 12.

$\boxed 8~~~\boxed{ 12}$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Determine the least common multiple of 8 and 12.

$\boxed 8~~~\boxed{ 12}$

Step-by-step solution

To find the least common multiple (LCM) of the numbers 8 and 12, we will list the multiples of each number and find the smallest multiple they have in common.

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

Multiples of 12: $12, 24, 36, 48, \ldots$

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 until you find the first common one: 24
Check: Verify 24 ÷ 8 = 3 and 24 ÷ 12 = 2 with no remainders ✓

Common Mistakes

Avoid these frequent errors

Choosing the first multiple that appears
Don't pick 8 or 12 just because they're multiples = wrong answer! These aren't divisible by both numbers. Always find the smallest number that appears in BOTH lists of multiples.

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

Is the LCM always bigger than both original numbers?

Usually yes! The LCM is typically larger than both numbers, like how 24 is bigger than both 8 and 12. The only exception is when one number divides evenly into the other.

What if I can't find a common multiple quickly?

Keep listing! Write out at least 5-6 multiples of each number. The LCM of small numbers like 8 and 12 will appear within the first few multiples.

Can I use prime factorization instead?

Yes! Factor both numbers: $8 = 2^3$ and $12 = 2^2 \times 3$ . Take the highest power of each prime: $2^3 \times 3 = 24$ .

How do I know when to stop listing multiples?

Stop when you find the first number that appears in both lists. That's your LCM! Don't keep going once you've found the common multiple.

What's the difference between LCM and GCF?

LCM finds the smallest multiple both numbers share, while GCF finds the largest factor both numbers share. LCM is usually bigger than your original numbers!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime