Calculate LCM: Finding the Least Common Multiple of 9, 4, and 6

Q: Why do I need to find prime factors first?

Prime factorization shows you the building blocks of each number! For 9, 4, and 6, you can see exactly which primes (2 and 3) and their powers you need to multiply.

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

Take the highest power of that prime! Since 4 = $ 2^2 $ and 6 = $ 2^1 \times 3^1 $, use $ 2^2 $ (not $ 2^1 $) in your LCM.

Q: Is there a faster way than prime factorization?

You can use the listing method (write multiples of each number), but prime factorization is more reliable for larger numbers and guarantees you won't miss the answer.

Q: What if I get confused about which power to use?

Make a table! List each prime factor and write the highest power that appears in any of the numbers. For our example: 2 appears as $ 2^2 $ (highest), 3 appears as $ 3^2 $ (highest).

Prime Factorization with Multiple Numbers

Calculate the least common multiple (LCM) for these numbers:

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

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the least common multiple (LCM) for these numbers:

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

Step-by-step solution

To find the least common multiple (LCM) of the numbers 9, 4, and 6, use their prime factors:

Prime factors of 9: $9 = 3^2$

Prime factors of 4: $4 = 2^2$

Prime factors of 6: $6 = 2^1 \times 3^1$

The LCM is the product of the highest powers of all prime factors:

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: LCM uses highest powers of all prime factors
Technique: Find $2^2 \times 3^2 = 4 \times 9 = 36$
Check: Verify 36 divides by 9, 4, and 6 evenly ✓

Common Mistakes

Avoid these frequent errors

Using lowest powers instead of highest
Don't take the lowest power of each prime like $2^1 \times 3^1 = 6$ = wrong LCM! This gives you a common factor, not the least common multiple. Always use the highest power of each prime factor that appears.

Practice Quiz

Test your knowledge with interactive questions

You have a pair of denominators, what is their least common multiple?

$\boxed 2~~~\boxed5$

FAQ

Everything you need to know about this question

Why do I need to find prime factors first?

Prime factorization shows you the building blocks of each number! For 9, 4, and 6, you can see exactly which primes (2 and 3) and their powers you need to multiply.

What if two numbers share the same prime factor?

Take the highest power of that prime! Since 4 = $2^2$ and 6 = $2^1 \times 3^1$ , use $2^2$ (not $2^1$ ) in your LCM.

How can I check if 36 is really the LCM?

Divide 36 by each original number: 36÷9=4, 36÷4=9, 36÷6=6. All give whole numbers, so 36 works! Also verify no smaller number works for all three.

Is there a faster way than prime factorization?

You can use the listing method (write multiples of each number), but prime factorization is more reliable for larger numbers and guarantees you won't miss the answer.

What if I get confused about which power to use?

Make a table! List each prime factor and write the highest power that appears in any of the numbers. For our example: 2 appears as $2^2$ (highest), 3 appears as $3^2$ (highest).

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