Find the LCM of 7 and 14: Least Common Multiple Practice

Q: Why isn't the LCM of 7 and 14 equal to 7 × 14?

Because 14 is already a multiple of 7! When one number divides evenly into another, the larger number is automatically the LCM. You only multiply when the numbers share no common factors.

Q: Is there a faster way than listing all multiples?

Yes! Use this formula: LCM = (a × b) ÷ GCD, where GCD is the Greatest Common Divisor. For 7 and 14: LCM = $ (7 × 14) ÷ 7 = 14 $

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

Never! The LCM must be divisible by both numbers, so it's always greater than or equal to the larger of the two numbers.

LCM with Multiple Relationships

What is the least common multiple of these two numbers?

$\boxed{7}~~~\boxed{14}$

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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?

$\boxed{7}~~~\boxed{14}$

Step-by-step solution

To find the least common multiple (LCM) of $7$ and $14$ , we list the multiples of each number:

Multiples of $7$ are $7, 14, 21, 28, \ldots$
Multiples of $14$ are $14, 28, 42, \ldots$

The smallest common multiple is $14$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: LCM is the smallest positive integer divisible by both numbers
Method: List multiples until you find the first common one: 7, 14, 21...
Check: Verify 14 ÷ 7 = 2 and 14 ÷ 14 = 1 with no remainders ✓

Common Mistakes

Avoid these frequent errors

Confusing LCM with multiplication
Don't just multiply the numbers together (7 × 14 = 98) = wrong answer! This only works when numbers share no common factors. Always find the actual least common multiple by listing multiples or using prime factorization.

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 7 and 14 equal to 7 × 14?

Because 14 is already a multiple of 7! When one number divides evenly into another, the larger number is automatically the LCM. You only multiply when the numbers share no common factors.

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

Divide the larger number by the smaller number. If you get a whole number with no remainder, then it's a multiple! Here: $14 ÷ 7 = 2$ exactly.

What if I can't tell which multiples to list?

Start with the larger number and check if it's divisible by the smaller one. If yes, that's your LCM! If no, then list multiples of the larger number: 14, 28, 42...

Is there a faster way than listing all multiples?

Yes! Use this formula: LCM = (a × b) ÷ GCD, where GCD is the Greatest Common Divisor. For 7 and 14: LCM = $(7 × 14) ÷ 7 = 14$

Can the LCM ever be smaller than both original numbers?

Never! The LCM must be divisible by both numbers, so it's always greater than or equal to the larger of the two numbers.

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