Question

Question

The least common multiple of 14 and 21 is:
(1 point)
Responses

294
294

21
21

7
7

42

Answer 1

The least common multiple (LCM) of two numbers can be found using the formula:

\[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \]

Where GCD is the greatest common divisor.

For the numbers 14 and 21:

• The factors of 14 are \(2 \times 7\).
• The factors of 21 are \(3 \times 7\).

The GCD of 14 and 21 is 7, since that is the highest number that divides both.

Now we can calculate the LCM:

\[ \text{LCM}(14, 21) = \frac{14 \times 21}{\text{GCD}(14, 21)} = \frac{14 \times 21}{7} = \frac{294}{7} = 42 \]

Thus, the least common multiple of 14 and 21 is 42.