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

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

LCM (Least Common Multiple) finds the smallest number both numbers can divide into evenly. GCF (Greatest Common Factor) finds the largest number that divides into both. For 8 and 12: LCM = 24, GCF = 4.

Q: Why can't the answer be 96 (8 × 12)?

While $ 8 \times 12 = 96 $ is a common multiple, it's not the least common multiple. We want the smallest number that both 8 and 12 divide into, which is 24.

Q: Is there a faster way than listing multiples?

Yes! You can use prime factorization: $ 8 = 2^3 $ and $ 12 = 2^2 \times 3 $. Take the highest power of each prime: $ 2^3 \times 3 = 24 $.

Q: What if one number is a multiple of the other?

If one number divides evenly into the other, the larger number is automatically the LCM. For example, LCM of 6 and 18 is simply 18 since 18 ÷ 6 = 3.

Q: How do I check if my LCM is correct?

Divide your LCM by each original numberBoth divisions should give whole numbers with no remaindersMake sure no smaller positive number works for both

LCM with List Method

What is the least common multiple of these two numbers?

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

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the least common multiple of these two numbers?

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

Step-by-step solution

To find the least common multiple (LCM) of $8$ and $12$ , we list the multiples of each number:

Multiples of $8$ are $8, 16, 24, 32, \ldots$
Multiples of $12$ are $12, 24, 36, \ldots$

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 both numbers divide into
List Method: Write multiples until you find the first common one: 8, 16, 24
Check: Verify 24 ÷ 8 = 3 and 24 ÷ 12 = 2 with no remainders ✓

Common Mistakes

Avoid these frequent errors

Confusing LCM with GCF (Greatest Common Factor)
Don't find the largest number that divides both = 4 instead of 24! LCM finds the smallest multiple they share, while GCF finds the largest factor they share. Always list multiples going up, not factors going down.

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

What's the difference between LCM and GCF?

LCM (Least Common Multiple) finds the smallest number both numbers can divide into evenly. GCF (Greatest Common Factor) finds the largest number that divides into both. For 8 and 12: LCM = 24, GCF = 4.

Why can't the answer be 96 (8 × 12)?

While $8 \times 12 = 96$ is a common multiple, it's not the least common multiple. We want the smallest number that both 8 and 12 divide into, which is 24.

Is there a faster way than listing multiples?

Yes! You can use prime factorization: $8 = 2^3$ and $12 = 2^2 \times 3$ . Take the highest power of each prime: $2^3 \times 3 = 24$ .

What if one number is a multiple of the other?

If one number divides evenly into the other, the larger number is automatically the LCM. For example, LCM of 6 and 18 is simply 18 since 18 ÷ 6 = 3.

How do I check if my LCM is correct?

Divide your LCM by each original number
Both divisions should give whole numbers with no remainders
Make sure no smaller positive number works for both

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