Find the L.C.M and H.C.F of the following pairs of integers and verify :

Question : Find the L.C.M and H.C.F of the following pairs of integers and verify :

L.C.M \(\times\) H.C.F = Product of the two numbers

(i)  26 and 91

(ii)  510 and 92

(iii)  336 and 54

Solution

(i)  26 and 91

26 = 2 \(\times\) 13        and       91 = 7 \(\times\) 13

\(\therefore\)   L.C.M of 26 and 91 = 2 \(\times\) 7 \(\times\) 13 = 182

and H.C.F of 26 and 91 = 13

Now,    182 \(\times\) 13 = 2366  and   26 \(\times\) 91 = 2366

Hence,    182 \(\times\) 13 = 26 \(\times\) 91

(ii)  510 and  92

510 = 2 \(\times\) 3 \(\times\) 5 \(\times\) 17      and       92 = 2 \(\times\) 2 \(\times\) 23

\(\therefore\)   L.C.M of 510 and 92 = 2 \(\times\) 2 \(\times\) 3 \(\times\) 5 \(\times\) 17 \(\times\) 23 = 23460

and H.C.F of 510 and 92 = 2

Now,    23460 \(\times\) 2 = 46920  and   510 \(\times\) 92 = 46920

Hence,    23460 \(\times\) 2 = 510 \(\times\) 92

(iii)  336 and 54

336 = 2 \(\times\) 2 \(\times\) 2 \(\times\) 2 \(\times\) 3 \(\times\) 7

and       54 = 2 \(\times\) 3 \(\times\) 3 \(\times\) 3

\(\therefore\)   L.C.M of 336 and 54 = 2 \(\times\) 2 \(\times\) 2 \(\times\) 2 \(\times\) 3 \(\times\) 3 \(\times\) 3 \(\times\) 7 = 3024

and H.C.F of 336 and 54 = 2 \(\times\) 3 = 6

Now,    3024 \(\times\) 6 = 18144  and   336 \(\times\) 54 = 18144

Hence,    3024 \(\times\) 6 = 336 \(\times\) 54

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