Question

Find the LCM and HCF of the following pair of integers and verify that LCM x HCF=product of the two numbers : 26 and 91 [2 MARK]

Answer 1

H.C.F : 0.5 Mark
L.C.M : 0.5 Mark
Verification : 1 Mark

Consider 26 and 91

26 = 2 $\times$13

91 = 7 $\times$13

HCF = Product of the smallest power of each common prime factor in the numbers = 13

LCM = Product of the greatest power of each prime factor involved in the numbers = 2 $\times$13 $\times$7 = 182

HCF $\times$ LCM =182 $\times$13 = 2366

Product of two given numbers = 26 $\times$ 91 = 2366

$\therefore$ It is proved that LCM $\times$ HCF = product of two numbers