A clock has two hands. The first hand completes a full rotation in 8 seconds, and the second hand completes a full rotation in 6 seconds. How long will it take for both hands to be at the top of the d

Time for the first hand to go around $= 8 \text{ seconds}$

$$8 = 2 \times 2 \times 2 = 2^3$$

Time for the second hand to go around $= 6 \text{ seconds}$

$$6 = 2 \times 3$$

The LCM is the product of the highest powers of all prime factors present in either number.

$$\text{LCM}(8, 6) = 2^3 \times 3^1 = 8 \times 3 = 24$$

The hands will next be together at the top of the dial after 24 seconds.

The hands will next be together at the top of the dial after $\text{24 seconds}$.