Calculate LCM: Finding the Least Common Multiple of 6, 8, and 9

Q: Why can't I just multiply all the numbers together?

Multiplying gives you $ 6 \times 8 \times 9 = 432 $, which is a common multiple but not the least one! The LCM is the smallest number that all given numbers divide into evenly.

Q: How do I know which power to choose?

Always take the highest power of each prime that appears. For example: if one number has $ 2^1 $ and another has $ 2^3 $, use $ 2^3 $ in your LCM.

Prime Factorization with Multiple Numbers

Given several denominators, what is their least common multiple?

$\boxed{6}~~~\boxed{8} ~~~\boxed{9}$

❤️ 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?

$\boxed{6}~~~\boxed{8} ~~~\boxed{9}$

Step-by-step solution

To find the least common multiple (LCM) of $6$ , $8$ and $9$ , we start by finding the prime factors of each number:

$6 = 2 \, \times \, 3$

$8 = 2^3$

$9 = 3^2$

The LCM is found by taking the highest power of each prime that appears in these factorizations:

$2^3$ (from 8), and $3^2$ (from 9).

The LCM is $2^3 \, \times \, 3^2 = 8 \, \times \, 9 = 72$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Find prime factors of each number using repeated division
Technique: Take highest power of each prime: $2^3$ from 8, $3^2$ from 9
Check: Verify LCM is divisible by all original numbers: 72÷6=12, 72÷8=9, 72÷9=8 ✓

Common Mistakes

Avoid these frequent errors

Adding all the numbers together
Don't just add 6+8+9=23! This gives you the sum, not the LCM. The LCM must be divisible by each number. Always use prime factorization and take the highest power of each prime factor.

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 all the numbers together?

Multiplying gives you $6 \times 8 \times 9 = 432$ , which is a common multiple but not the least one! The LCM is the smallest number that all given numbers divide into evenly.

What if I can't remember all the prime numbers?

Start with small primes: 2, 3, 5, 7, 11... For numbers like 6, 8, 9, you only need 2 and 3. Keep dividing until you can't divide evenly anymore!

How do I know which power to choose?

Always take the highest power of each prime that appears. For example: if one number has $2^1$ and another has $2^3$ , use $2^3$ in your LCM.

What if two numbers share the same prime factor?

That's normal! Like 6 and 9 both have factor 3. Just use the higher power: 6 has $3^1$ , 9 has $3^2$ , so use $3^2$ .

Can I use a different method besides prime factorization?

Yes! You can list multiples of each number and find the smallest common one, but prime factorization is faster and works better with larger 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