A class VI mathematics teacher posed the following problem to her students :…

Concept

If several people have different step lengths and each must cover the same total distance using only a whole number of their own steps, that distance has to be a common multiple of every step length. The smallest distance that works for everyone is the Least Common Multiple (LCM) of the step lengths.

Application

1. Write each step length in prime-factorised form: 70 = 2 × 5 × 7, 85 = 5 × 17, and 95 = 5 × 19.

2. Take the highest power of every prime that appears across the three numbers: 2, 5, 7, 17 and 19 (each to the first power).

3. Multiply these together to get the LCM: 2 × 5 × 7 × 17 × 19 = 22,610.

4. So 22,610 cm is the minimum distance in which all three persons' steps (70 cm, 85 cm and 95 cm) fit an exact whole number of times — finding this distance is exactly what the concept of LCM is used for.

Why the other options don't fit

• Concept of HCF: HCF finds the greatest length that divides two or more given lengths exactly — useful for splitting things into the largest equal parts, not for finding a distance that is a multiple of several different lengths.

• Concept of division: Division converts one known distance into a step count for a single step length; it does not by itself identify which distance simultaneously gives a whole number of steps for all three step lengths together.

• Concept of proportion: Proportion deals with two ratios being equal to each other; the three step lengths here are not being compared as a scaling ratio, so proportion does not identify the required common distance.

The concept a teacher must draw on here is the Concept of LCM.