Question

Find the HCF and LCM of the following pairs of number and verify that product of the number = H.C.F × L.C.M.
(a) 13,39
(b) 15,4
(c) 21,24​

Answer 1

Solution

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(i) 26 and 91

Factor of 26=2×13×1

Factor of 91=7×13×1

HCF of 26 and 91=13×1=13

LCM of 26 and 91=2×7×13=182

LCM × HCF =182×13=2366

26×91=2366

So, LCM.HCF = product of the two numbers =26×91.

Hence proved.

(ii) 510×92

Factor of 510=2×3×5×17×1

Factor of 92=2×2×23

HCF of 510 and 92=2×2=2

LCM of 510 and 92=2×2×3×5×17×23=23,460

LCM × HCF =23,460×2=46,920

510×92=46,920

So, LCM.HCF = product of the two numbers =510×92.

Hence proved.

(iii) 336 and 54

Factor of 336=2×2×2×2×7×3×1

Factor of 54=2×3×3×3

HCF of 336 and 54=2×3=6

LCM of 336 and 54=2×3×2×2×2×7×3×3=3,024

LCM × HCF =3,024×6=18,144

366×54=18,144

So, LCM.HCF = product of the two numbers =336×54.

Hence proved.