Three persons steps off from a pint. Their steps measure 40 cms, 42 cms and 45 cms respectively. At what distance will they be together again if their speeds are same?
To find the distance at which they will be together again, we need to calculate the least common multiple (LCM) of their step lengths.
Step 1: Determine the prime factors of each step length.
- The prime factors of 40 are 2 × 2 × 2 × 5 = 2³ × 5
- The prime factors of 42 are 2 × 3 × 7
- The prime factors of 45 are 3 × 3 × 5 = 3² × 5
Step 2: Write down the highest powers of each prime factor that appear in the factorization.
- The highest power of 2 that appears is 2³ = 8
- The highest power of 3 that appears is 3² = 9
- The highest power of 5 that appears is 5
Step 3: Multiply the highest powers of the prime factors together to find the LCM.
LCM = 2³ × 3² × 5 = 8 × 9 × 5 = 360
Therefore, the three persons will be together again at a distance of 360 cm.