Question

Diya and her mother go for a walk one morning. Diya takes a stride of 20 cm each time she takes a step and her mother takes a stride of 25 cm per step. What is the least distance covered after which both Diya and her mother will step together?
[The answer to this question is 100 cm]

Answer 1

$$\begin{gathered} \mathrm{Diya}\mathrm{takes}\mathrm{a}\mathrm{stride}\mathrm{of}20\mathrm{cm}\mathrm{and}\mathrm{her}\mathrm{mother}\mathrm{takes}\mathrm{a}\mathrm{stride}\mathrm{of}25\mathrm{cm}. \\ \mathrm{Least}\mathrm{distance}\mathrm{covered}\mathrm{after}\mathrm{which}\mathrm{both}\mathrm{will}\mathrm{step}\mathrm{together}=\mathrm{LCM}\mathrm{of}20\mathrm{cm}\mathrm{and}25\mathrm{cm} \\ \mathrm{Now},20=2\times 2\times 5\mathrm{and}25=5\times 5 \\ \mathrm{LCM}\mathrm{of}20\mathrm{and}25=2\times 2\times 5\times 5=100 \\ \mathrm{Therefore},\mathrm{LCM}\mathrm{of}20\mathrm{cm}\mathrm{and}25\mathrm{cm}=100\mathrm{cm} \\ \mathrm{Hence},\mathrm{least}\mathrm{distance}\mathrm{covered}\mathrm{after}\mathrm{which}\mathrm{both}\mathrm{will}\mathrm{step}\mathrm{together}\mathrm{is}100\mathrm{cm}. \end{gathered}$$