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.