Q2 of 54 Page 8

Find the LCM and HCF of the following integers by the prime factorization method.

(i) 12, 15 and 21


(ii) 17, 23 and 29


(iii) 8, 9 and 25


(iv) 72 and 108


(v) 306 and 657

I. 12,15 and 21


12 = 22×3


15 = 3×5


21 = 3×7


LCM = 22×3×5×7 = 420


HCF = 3


II. 17,23 and 29


17 = 1×17


23 = 1×23


29 = 1×29


LCM = 1×17×23×29 = 11339


HCF = 1


III. 8, 9 and 5


8 = 23


9 = 32


5 = 1×5


LCM = 23×32×5 = 360


HCF = 1


IV. 72 and 108


72 = 23×32


108 = 22×33


LCM = 25×35 = 7776


HCF = 22×32 = 4×9 = 36


V. 306 and 657


306 = 2×32×17


657 = 32×73


LCM = 2×32×17×73 = 22338


HCF = 32 = 9


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