Find the LCM: Calculating Least Common Multiple of 5 and 10

Q: Why isn't the LCM of 5 and 10 equal to 5 × 10 = 50?

You only multiply the numbers when they share no common factors. Since 10 is already a multiple of 5, the LCM is just 10, not 50!

Q: What if I can't see the pattern in the multiples?

Keep listing multiples until you find a match! For 5: 5, 10, 15, 20... For 10: 10, 20, 30... The first common one is your LCM.

Q: Is there a faster way than listing multiples?

Yes! Use the formula: $ LCM = \frac{a \times b}{GCF(a,b)} $. For 5 and 10: $ LCM = \frac{5 \times 10}{5} = 10 $

Q: 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.

LCM Calculation with Factor Relationships

What is the least common multiple of these two numbers?

$\boxed{5}~~~\boxed{10}$

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Step-by-step written solution

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Understand the problem

What is the least common multiple of these two numbers?

$\boxed{5}~~~\boxed{10}$

Step-by-step solution

To find the least common multiple (LCM) of $5$ and $10$ , we list the multiples of each number:

Multiples of $5$ are $5, 10, 15, 20, \ldots$
Multiples of $10$ are $10, 20, 30, \ldots$

The smallest common multiple is $10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: LCM is the smallest positive number divisible by all given numbers
Technique: List multiples of each number: 5 → 5, 10, 15; 10 → 10, 20, 30
Check: Verify 10 ÷ 5 = 2 and 10 ÷ 10 = 1 (both whole numbers) ✓

Common Mistakes

Avoid these frequent errors

Confusing LCM with GCF
Don't find the greatest common factor (GCF = 5) instead of LCM! This gives the largest number that divides both, not the smallest multiple they share. Always find the smallest number that BOTH numbers 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 isn't the LCM of 5 and 10 equal to 5 × 10 = 50?

You only multiply the numbers when they share no common factors. Since 10 is already a multiple of 5, the LCM is just 10, not 50!

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

Check if the larger number divides evenly by the smaller one. Since $10 ÷ 5 = 2$ with no remainder, 10 is a multiple of 5.

What if I can't see the pattern in the multiples?

Keep listing multiples until you find a match! For 5: 5, 10, 15, 20... For 10: 10, 20, 30... The first common one is your LCM.

Is there a faster way than listing multiples?

Yes! Use the formula: $LCM = \frac{a \times b}{GCF(a,b)}$ . For 5 and 10: $LCM = \frac{5 \times 10}{5} = 10$

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.

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