Find the lcm and hcf of the following pairs of integers and verify that lcm × hcf = product of the two numbers. (1) 26 & 91(2)510 & 92(3)336 & 54

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.

No a triangle cannot be formed because when you add the two smallest number together (which would be 11) the have to be bigger than the number it is "against" ( which would be 12)