# 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