Find the LCM of Denominators: Calculating LCM(3, 4, 6)

Q: Why isn't 6 the LCM since it's the largest number?

The LCM must be divisible by all numbers. Since $ 6 ÷ 4 = 1.5 $ (not a whole number), 6 cannot be the LCM.

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

Stop when you find the first number that appears in all three lists. That's your LCM! In this case, 12 appears first in all lists.

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

Yes! You can use prime factorization: $ 3 = 3, 4 = 2^2, 6 = 2 \times 3 $. Take the highest power of each prime: $ 2^2 \times 3 = 12 $.

Q: What if I got 24 as my answer?

While 24 is a common multiple of 3, 4, and 6, it's not the least common multiple. Remember, we want the smallest number that works!

LCM Calculation with Multiple Denominators

Given several denominators, what is their least common multiple?

$\boxed{3} \boxed{4} \boxed{6}$

❤️ 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

Given several denominators, what is their least common multiple?

$\boxed{3} \boxed{4} \boxed{6}$

Step-by-step solution

The least common multiple (LCM) of $3, 4, \text{ and } 6$ is the smallest positive integer that is divisible by each of these numbers.

First, list the multiples of each number:

Multiples of $3$ : 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of $4$ : 4, 8, 12, 16, 20, 24, ...
Multiples of $6$ : 6, 12, 18, 24, ...

The common multiples of $3, 4, \text{ and } 6$ are 12, 24, ...

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 all given numbers
Method: List multiples until finding the first common one like 12
Verification: Check that 12 ÷ 3 = 4, 12 ÷ 4 = 3, 12 ÷ 6 = 2 ✓

Common Mistakes

Avoid these frequent errors

Choosing the largest given number as the LCM
Don't assume the LCM is just the biggest number like 6! The number 6 isn't divisible by 4, so it can't be the LCM. Always find the smallest number that ALL given numbers divide into evenly.

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 6 the LCM since it's the largest number?

The LCM must be divisible by all numbers. Since $6 ÷ 4 = 1.5$ (not a whole number), 6 cannot be the LCM.

How do I know when to stop listing multiples?

Stop when you find the first number that appears in all three lists. That's your LCM! In this case, 12 appears first in all lists.

Is there a faster way than listing all multiples?

Yes! You can use prime factorization: $3 = 3, 4 = 2^2, 6 = 2 \times 3$ . Take the highest power of each prime: $2^2 \times 3 = 12$ .

What if I got 24 as my answer?

While 24 is a common multiple of 3, 4, and 6, it's not the least common multiple. Remember, we want the smallest number that works!

Why do we need to find the LCM of denominators?

Finding the LCM of denominators helps you add or subtract fractions by giving you a common denominator. It's essential for fraction operations!

🌟 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