Calculate LCM: Finding the Least Common Multiple of Denominators 8 and 5

Q: Why can't I just multiply 8 × 5 to get the LCM?

You can in this case because 8 and 5 are coprime (share no common factors)! When numbers have no common factors, their LCM equals their product. But this shortcut doesn't work for numbers like 6 and 9.

Q: What if the numbers share common factors?

When numbers share factors, their LCM is less than their product. For example, LCM(6,9) = 18, not 54, because they both contain factor 3.

Q: How do I find prime factorization quickly?

Start with the smallest prime (2) and keep dividing: 8 = 2 × 4 = 2 × 2 × 2 = 2³. Since 5 is already prime, we're done!

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

LCM finds the smallest number both divide into, while GCD finds the largest number that divides both. For 8 and 5: LCM = 40, GCD = 1.

Prime Factorization with Coprime Integers

Given two denominators, what is their least common multiple?

$\boxed{8}~~~\boxed{5}$

❤️ 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 two denominators, what is their least common multiple?

$\boxed{8}~~~\boxed{5}$

Step-by-step solution

To find the least common multiple (LCM) of 8 and 5, identify the prime factors:

$8 = 2^3$

$5 = 5$

The LCM is the product of the highest power of each prime:

$2^3 \times 5 = 8 \times 5 = 40$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Find prime factorization of each number first
Technique: Use highest power of each prime: $2^3 \times 5 = 40$
Check: Verify both numbers divide evenly: 40 ÷ 8 = 5, 40 ÷ 5 = 8 ✓

Common Mistakes

Avoid these frequent errors

Simply multiplying the two numbers together
Don't just calculate 8 × 5 = 40 without checking if they share factors! For numbers like 6 and 4, this gives 24 instead of the correct LCM of 12. Always find prime factorization first to identify the true least common multiple.

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 8 × 5 to get the LCM?

You can in this case because 8 and 5 are coprime (share no common factors)! When numbers have no common factors, their LCM equals their product. But this shortcut doesn't work for numbers like 6 and 9.

What if the numbers share common factors?

When numbers share factors, their LCM is less than their product. For example, LCM(6,9) = 18, not 54, because they both contain factor 3.

How do I find prime factorization quickly?

Start with the smallest prime (2) and keep dividing: 8 = 2 × 4 = 2 × 2 × 2 = 2³. Since 5 is already prime, we're done!

What's the difference between LCM and GCD?

LCM finds the smallest number both divide into, while GCD finds the largest number that divides both. For 8 and 5: LCM = 40, GCD = 1.

Can the LCM ever be smaller than both numbers?

Never! The LCM must be divisible by both numbers, so it's always greater than or equal to the larger number. The smallest possible LCM is the larger number itself.

🌟 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