Find the LCM of Denominators: 5, 4, and 6

Q: Why can't I just multiply 5 × 4 × 6 = 120?

While 120 is a common multiple, it's not the least common multiple! Since 4 and 6 both contain the factor 2, multiplying them together counts that factor twice. The LCM method avoids this duplication.

Q: How do I find prime factors of numbers like 4 and 6?

Break them down step by step: $ 4 = 2 \times 2 = 2^2 $ and $ 6 = 2 \times 3 $. Keep dividing by the smallest prime until you can't divide anymore!

Q: How do I know which power to use for each prime?

Always take the highest power that appears. For example, if you see $ 2^1 $ and $ 2^2 $, use $ 2^2 $ in your LCM.

LCM Finding with Multiple Denominators

Given three denominators, what is their least common multiple?

$\boxed{5}~~~\boxed{4}~~~\boxed{6}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given three denominators, what is their least common multiple?

$\boxed{5}~~~\boxed{4}~~~\boxed{6}$

Step-by-step solution

To find the least common multiple (LCM) of 5, 4, and 6, identify the prime factors:

$5 = 5$

$4 = 2^2$

$6 = 2 \times 3$

The LCM is obtained by taking the highest power of each prime:

$5 \times 2^2 \times 3 = 60$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Prime Factorization: Break each number into its prime factors completely
Technique: Take highest power of each prime: $5^1 \times 2^2 \times 3^1 = 60$
Check: Verify 60 divides evenly by all denominators: 60÷5=12, 60÷4=15, 60÷6=10 ✓

Common Mistakes

Avoid these frequent errors

Simply multiplying all denominators together
Don't just multiply 5 × 4 × 6 = 120! This gives a common multiple but not the LEAST common multiple. The LCM is smaller because numbers share common factors. Always use prime factorization and take only the highest power of each prime.

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 5 × 4 × 6 = 120?

While 120 is a common multiple, it's not the least common multiple! Since 4 and 6 both contain the factor 2, multiplying them together counts that factor twice. The LCM method avoids this duplication.

How do I find prime factors of numbers like 4 and 6?

Break them down step by step: $4 = 2 \times 2 = 2^2$ and $6 = 2 \times 3$ . Keep dividing by the smallest prime until you can't divide anymore!

What if one of the numbers is already prime, like 5?

Perfect! Prime numbers are already in their simplest form. So $5 = 5^1$ - just include it once in your LCM calculation.

How do I know which power to use for each prime?

Always take the highest power that appears. For example, if you see $2^1$ and $2^2$ , use $2^2$ in your LCM.

Can I check my LCM answer?

Yes! Your LCM should divide evenly into each original number. Try: $60 ÷ 5 = 12$ , $60 ÷ 4 = 15$ , $60 ÷ 6 = 10$ - all whole numbers! ✓

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