Final answer:
The minimum distance Athul, Ravi, and Tarun should walk so that each can cover the same distance in complete steps is the least common multiple (LCM) of their step lengths, which is 840 cm.
Step-by-step explanation:
The question involves finding the minimum common multiple of the step lengths of Athul, Ravi, and Tarun to determine the minimum distance they should walk so that each can cover the same distance in a complete step. The step lengths are 40 cm, 42 cm, and 45 cm, respectively. Finding the least common multiple (LCM) of the three given numbers will give us the answer to the question.
To find the LCM of 40, 42, and 45, we list out the prime factors for each number:
- 40 = 23 × 5
- 42 = 2 × 3 × 7
- 45 = 32 × 5
We then take the highest power of each prime number from the factorizations to find the LCM:
LCM = 23 × 32 × 5 × 7 = 840 cm
Therefore, the minimum distance they all need to walk to have complete steps for each person is 840 cm, which corresponds to option C. So, Athul, Ravi, and Tarun should all walk at least 840 cm to ensure they can all take whole steps without any remainder.