15 Two alarm clocks ring their alarm at regular intervals of \( 50 sec \) and \( 48 sec \). If they first beep together at time?

Question

15 Two alarm clocks ring their alarm at regular intervals of \( 50 sec \) and \( 48 sec \). If they first beep together at tive?

Answer 1

The first time they beep together is LCM(50,48).

For LCM:

50 = 2 × 5 × 5 = 5² × 2

48 = 2 × 2 × 2 × 2 × 3 = 2⁴ × 3

We can see that common factors are: 2¹ only

So, LCM = (2¹) × (2³ × 3 × 5²) = 1200 sec

Hence, they beep together after 1200 sec for the first time.