Question

Three friends plan to go for a morning walk. They step off together and their steps measures 48 cm, 52 cm and 56 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps ten times?

Answer 1

Given:
- Step lengths: 48 cm, 52 cm, 56 cm.
- Each walks the same distance in complete steps, 10 times.

Step 1: Find LCM of step lengths
The minimum distance (one walk) is the LCM of step lengths to ensure an integer number of steps for each.
Prime factorization:
\[48 = 2^4 \times 3\] \[52 = 2^2 \times 13\] \[56 = 2^3 \times 7\]
LCM: product of highest prime powers:
\[\text{LCM} = 2^4 \times 3 \times 7 \times 13 = 16 \times 3 \times 7 \times 13\] Calculate:
\[16 \times 3 = 48, \quad 48 \times 7 = 336, \quad 336 \times 13 = 4368\, \text{cm}\]

Step 2: Calculate total distance (10 walks)
Total distance for each friend:
\[\text{Total distance} = 10 \times 4368 = 43680\, \text{cm}\]

Step 3: Convert to meters (optional)
\[43680\, \text{cm} = \frac{43680}{100} = 436.8\, \text{meters}\]

Final Answer:
Minimum distance each should walk:
\[\boxed{43680\, \text{cm} \text{ or } 436.8\, \text{meters}}\]