Find the LCM: Calculating Least Common Multiple of 4 and 8

Q: Why isn't the LCM of 4 and 8 equal to 4 × 8 = 32?

Because $ 32 $ isn't the least common multiple! While 32 is a common multiple, $ 8 $ is smaller and also works since both 4 and 8 divide evenly into 8.

Q: How do I know when one number is a multiple of another?

When one number divides evenly into another! Since $ 8 ÷ 4 = 2 $ with no remainder, 8 is a multiple of 4. This makes the LCM simply the larger number.

Q: Can the LCM ever be smaller than both original numbers?

No! The LCM must be at least as large as the biggest original number, since it needs to contain all factors of both numbers.

Least Common Multiple with Simple Factors

What is the least common multiple of these two numbers?

$\boxed{4}~~~\boxed{8}$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the least common multiple of these two numbers?

$\boxed{4}~~~\boxed{8}$

Step-by-step solution

To find the least common multiple (LCM) of $4$ and $8$ , we list the multiples of each number:

Multiples of $4$ are $4, 8, 12, 16, 20, \ldots$
Multiples of $8$ are $8, 16, 24, \ldots$

The smallest common multiple is $8$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: List multiples of each number until you find the smallest common one
Technique: Multiples of 4: 4, 8, 12... Multiples of 8: 8, 16, 24...
Check: Verify 8 is divisible by both 4 and 8: 8÷4=2, 8÷8=1 ✓

Common Mistakes

Avoid these frequent errors

Multiplying the numbers together instead of finding LCM
Don't just multiply 4 × 8 = 32! This gives you a common multiple, but not the least one. The LCM of 4 and 8 is actually 8, not 32. Always list multiples systematically to find the smallest shared one.

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 isn't the LCM of 4 and 8 equal to 4 × 8 = 32?

Because $32$ isn't the least common multiple! While 32 is a common multiple, $8$ is smaller and also works since both 4 and 8 divide evenly into 8.

How do I know when one number is a multiple of another?

When one number divides evenly into another! Since $8 ÷ 4 = 2$ with no remainder, 8 is a multiple of 4. This makes the LCM simply the larger number.

What's the fastest way to find LCM of two numbers?

Check if the larger number is divisible by the smaller one first! If yes, the LCM is the larger number. If no, then list multiples of both numbers.

Can the LCM ever be smaller than both original numbers?

No! The LCM must be at least as large as the biggest original number, since it needs to contain all factors of both numbers.

What if I need the LCM of more than two numbers?

Use the same method! List multiples and find the smallest one that all numbers divide into evenly. Or find LCM of two numbers first, then find LCM of that result with the third number.

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