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 of three friends: 48 cm, 52 cm, and 56 cm.
- Each wants to walk the same distance in complete steps exactly 10 times.

Step 1: Find least common multiple (LCM) of step lengths
The minimum distance they should walk (one time) is the LCM of their step lengths so that each covers an integer number of steps.
Find prime factorization:
\[ 48 = 2^4 \times 3 \] \[ 52 = 2^2 \times 13 \] \[ 56 = 2^3 \times 7 \]
LCM is product of highest powers of all primes:
\[ \text{LCM} = 2^4 \times 3 \times 7 \times 13 = 16 \times 3 \times 7 \times 13 \] Calculate:
\[ 16 \times 3 = 48, \quad 48 \times 7 = 336, \quad 336 \times 13 = 4368\, \text{cm} \]

Step 2: Calculate total distance for 10 times
Each friend wants to walk the distance 10 times,
\[ \text{Total distance} = 10 \times 4368 = 43680\, \text{cm} \]

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

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