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Question

Evaluate :

(i) 37+49+117+79(ii) 23+45+13+25(iii) 47+0+89+137+179(iv) 38+512+37+312+58+27

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Solution

(i) 37+49+117+79=(37+117+)+(49+79)=3117+4+79=87+39=87+13

LCM of 3 and 2=3×7=21=8×37×3+1×73×7 (LCM of 7 and 3=21)=24+721=1721(ii)23+45+13+25=(23+13)+(45+25)=2+13+4+25=33+(25)

LCM of 3 and 5=3×5=15=3×53×5+2×35×3 (LCM of3 and 5=15)=15615=915=35(iii) 47+089+137+179=47+89+137+179=[47+(137)]+(89+179)=(47)137+(89)+179=97+99=97+1=9×17×1+1×71×7 (LCM of 1 and 7=7)=97+77=27(iv) 38+512+37+312+58+27=(3858)+(512+312)+(3727)=28212+17=14+16+17

LCM of 4.6 and 7=2×2×3×7=84=1×214×211×146×14+1×127×12 (LCM of 4,6 and 7=84)=2114+1284=35+1284=2384


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