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Question

Find the H.C.F and L.C.M of the following by the fundamental theorem of arithmetic.

(i) 9 and 12
(ii) 60 and 72
(iii) 8624 and 21658
(iv) 12, 30, 144
(v) 17, 13, 29

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Solution

(i) 9 = 3×3=32 12=2×2×3=22×31HCF of 9 and 12 =31=3LCM of 9 and 12 =22×32=4×9=36


(ii) 60 = 2×2×3×5=22×31×51 72=2×2×2×3×3=23×32HCF of 60 and 72 =22×31=2×2×3=12LCM of 60 and 72 =23×32×51=8×9×5=360



(iii) 8624 =2×2×2×2×7×7×11= 24×72×11 21658=2×7×7×13×17=21×72×13×17HCF of 8624 and 21658 =21×72=2×49=98LCM of 8624 and 21658 =24×72×11×13×17 =16×49×11×13×17 =1905904

(iv) 12= 2×2×3=22×31 30 =2×3×5=21×31×51 144=2×2×2×2×3×3=24×32HCF of 12,30 and 144=2×3=6LCM of 12,30 and 144 =24×32×51=720

(v) 17 = 171×1 23 =231×1 29=291×1HCF of 17,23 and 29 =1LCM of 17,23 and 29 =17×23×29=11339

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