Question

find the lcm and hcf of the integers 26 and 91 and verify that lcm × hcf = 26 × 91​

Answer 1

Answer:

Step-by-step explanation:

26=2*13

91=7*13

so HCF=13

and LCM=2*7*13=182

hcf*lcm=13*182=13*2*91

=26*91

hcf*lcm=26 * 91

Answer 2

By prime factorisation,

26 = 2¹ × 13¹

91 = 7¹ × 13¹

Now, HCF(26, 91) = 13

Also, LCM(26, 91) = 2¹ × 13¹ × 7¹.

Now we have to verify that,

LCM(26, 91) × HCF(26, 91) = 26 × 91

{LCM(a, b) · HCF(a, b) = a · b}

LHS:

(2 × 13 × 7)(13)

= 2 × 13 × 7 × 13

= 26 × 91

RHS:

= 26 × 91 = LHS.

Hence, proved.