Question

Find H.C.F of 90 and 126 by Euclid division algorithm.Also find their L.C.M and verify that L.C.M * H.C.F =product if two number.

Answer 1

Dear student

$$\begin{gathered} 126=90\times 1+36 \\ 90=36\times 2+18 \\ 36=2\times 18+0 \\ \mathrm{So},\mathrm{hcf}\mathrm{of}126\mathrm{and}90\mathrm{is}18 \\ 90=2\times 3\times 3\times 5 \\ 126=2\times 3\times 3\times 7 \\ \mathrm{Lcm}\mathrm{of}90\mathrm{and}126=2\times 3\times 3\times 5\times 7=630 \\ \mathrm{Now}\mathrm{consider}\mathrm{lcm}\times \mathrm{hcf}=18\times 630=11340 \\ \mathrm{Product}\mathrm{of}126\mathrm{and}90\mathrm{ie}126\times 90=11340 \\ \mathrm{So},\mathrm{lcm}\times \mathrm{hcf}=\mathrm{Product}\mathrm{of}126\mathrm{and}90 \end{gathered}$$
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