Find the LCM of 4 and 6: Least Common Multiple Practice

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

LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly. GCD (Greatest Common Divisor) is the largest number that divides into both numbers. Think: LCM goes up, GCD goes down!

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

Yes! Use prime factorization: 4 = 2² and 6 = 2×3. Take the highest power of each prime: 2² × 3 = 12. This method works great for larger numbers!

Q: Can the LCM ever be smaller than both numbers?

Never! The LCM must be at least as large as the bigger number. If you get an answer smaller than both original numbers, you've made an error.

Q: What if one number divides evenly into the other?

Then the larger number is the LCM! For example, LCM of 3 and 12 is just 12, since 12 is already a multiple of 3.

LCM Methods with Prime Factorization

You have two numbers, 4 and 6. What is their least common multiple?

$\boxed 4~~~\boxed 6$

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Step-by-step written solution

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Understand the problem

You have two numbers, 4 and 6. What is their least common multiple?

$\boxed 4~~~\boxed 6$

Step-by-step solution

To find the least common multiple (LCM) of the numbers 4 and 6, list the multiples of each number and find the smallest multiple they have in common.

Multiples of 4: $4, 8, 12, 16, \ldots$

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

The smallest common multiple is $12$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: LCM is the smallest number divisible by both numbers
Technique: List multiples: 4: 4,8,12... and 6: 6,12,18... find common
Check: Verify 12÷4=3 and 12÷6=2 with no remainders ✓

Common Mistakes

Avoid these frequent errors

Finding GCD instead of LCM
Don't find the greatest common divisor (2) = wrong answer! GCD finds the largest factor they share, but LCM finds the smallest multiple they share. Always list multiples, not factors, to find LCM.

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 GCD?

LCM (Least Common Multiple) is the smallest number that both numbers divide into evenly. GCD (Greatest Common Divisor) is the largest number that divides into both numbers. Think: LCM goes up, GCD goes down!

Is there a faster way than listing all multiples?

Yes! Use prime factorization: 4 = 2² and 6 = 2×3. Take the highest power of each prime: 2² × 3 = 12. This method works great for larger numbers!

Can the LCM ever be smaller than both numbers?

Never! The LCM must be at least as large as the bigger number. If you get an answer smaller than both original numbers, you've made an error.

What if one number divides evenly into the other?

Then the larger number is the LCM! For example, LCM of 3 and 12 is just 12, since 12 is already a multiple of 3.

How do I check if my LCM answer is correct?

Divide your answer by each original number. If both divisions give whole numbers with no remainders, your LCM is correct! For 4 and 6: $12 ÷ 4 = 3$ and $12 ÷ 6 = 2$ ✓

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