Find the LCM of Denominators: 4, 6, 9, and 3

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

While 4×6×9×3 = 648 works as a common multiple, it's not the smallest one! The LCM method finds the most efficient common denominator, making fraction operations much easier.

Q: What if two numbers share the same prime factor?

That's exactly why we use highest powers! For example, both 4 and 6 contain the factor 2, so we only need $ 2^2 $ (the highest power) in our LCM.

Q: What if one of my numbers is already a prime?

No problem! Like with 3 in this example, just write it as $ 3^1 $. Prime numbers are their own prime factorization.

Q: Can I use this method with more than 4 numbers?

Absolutely! The prime factorization method works for any quantity of numbers. Just find all prime factors and take the highest power of each.

LCM Finding with Multiple Denominators

Given four denominators, what is their least common multiple?

$\boxed{4}~~~\boxed{6}~~~\boxed{9}~~~\boxed{3}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given four denominators, what is their least common multiple?

$\boxed{4}~~~\boxed{6}~~~\boxed{9}~~~\boxed{3}$

Step-by-step solution

To find the least common multiple (LCM) of 4, 6, 9, and 3, we start by identifying the prime factors:

$4 = 2^2$

$6 = 2 \times 3$

$9 = 3^2$

$3 = 3$

The LCM will be found by taking the highest power of each prime present:

$2^2 \times 3^2 = 4 \times 9 = 36$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Prime Factorization: Break each number into prime factors first
Technique: Take highest power of each prime: $2^2 \times 3^2 = 36$
Check: Verify 36 divides evenly by all numbers: 36÷4=9, 36÷6=6, 36÷9=4, 36÷3=12 ✓

Common Mistakes

Avoid these frequent errors

Multiplying all denominators together
Don't just multiply 4×6×9×3 = 648! This gives a common multiple but not the LEAST common multiple. Always use prime factorization to find the smallest number that all denominators 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 can't I just multiply all the denominators together?

While 4×6×9×3 = 648 works as a common multiple, it's not the smallest one! The LCM method finds the most efficient common denominator, making fraction operations much easier.

What if two numbers share the same prime factor?

That's exactly why we use highest powers! For example, both 4 and 6 contain the factor 2, so we only need $2^2$ (the highest power) in our LCM.

How do I know which power is the highest?

Compare the exponents for each prime across all factorizations. For 2: we see $2^2$ and $2^1$ , so choose $2^2$ . For 3: we see $3^2$ and $3^1$ , so choose $3^2$ .

What if one of my numbers is already a prime?

No problem! Like with 3 in this example, just write it as $3^1$ . Prime numbers are their own prime factorization.

Can I use this method with more than 4 numbers?

Absolutely! The prime factorization method works for any quantity of numbers. Just find all prime factors and take the highest power of each.

How do I check if my LCM is correct?

Divide your LCM by each original number. If all divisions result in whole numbers, your LCM is correct! Also verify no smaller number works by testing a few numbers below your answer.

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