Sol. (1) Prime factors of 26 = 2 x 13 Prime factors of 91 = 7 x 13 Hence, HCF = Common factors between 26 and 91 =13 and LCM=13x2x7=182
Now product of numbers 26 and 91 = 26 x 91 = 2366 and Product of HCF and LCM = 13 x 182 = 2366
So, it verify that product of two numbers = Product of HCF and LCM.
(2) Prime factors of 510 = 2 x 3 x 5 x 17 Prime factors of 92 = 2 x 2 x 23 Hence,HCF=2 and LCM=2×2×3 × 5×17×23 =23460
Now product of Numbers 510 and 92 = 46920 and product of HCF and LCM = 2 x 23460= 46920
Hence, verified that product of two numbers 18 equal to product of their HCF and LCM.
(3) Prime factors of336 = 2 x 2 x 2 x 2 x 3 x 7
Prime factors of 54 = 2 x 3 x 3 x 3 Hence, HCF (Product of common factors of 336 and 54) =2 x 3=6
And LCM (Product of all common factors with remaining factors) =(2 x 3)x 2 x 2 x 2 x 3 x 3 x 7=3024
Now, product of numbers 336 and 54 = 336 x 54 = 18144 and product of HCF and LCM = 6 x 3024 = 18144 Hence, product of two numbers: Product of HCF and LCM.
