Question

At the gym, Hina swims every 16 days, runs every 42 days, and cycles every 36 days. If she did all three activities today, in how many days will she do all three activities again on the same day?

In a morning walk, three persons step off together. Their steps measure 75 cm, 80 cm, and 90 cm, respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

Answer 1

Hina will do all three activities again on the same day in 1008 days.

Step-by-step explanation:

To find out how many days it will take for Hina to do all three activities again on the same day, we need to find the least common multiple (LCM) of 16, 42, and 36. The LCM is the smallest number that is evenly divisible by all three numbers.

The prime factorization of 16 is 2 * 2 * 2 * 2, the prime factorization of 42 is 2 * 3 * 7, and the prime factorization of 36 is 2 * 2 * 3 * 3. We take the highest power of each prime factor that appears in any of the three numbers and multiply them together: 2^4 * 3^2 * 7 = 16 * 9 * 7 = 1008.

Therefore, Hina will do all three activities again on the same day in 1008 days.