Question

consider two positive integers a and b then LCM × HCF =a× b prove​

Answer 1

let a and b are two integers

lcm of a and b are ab.....(i)

hcf of a and b are 1 because there is only 1 in a and b are common factor of both .....(ii)

product of lcm and hcf of a and b=ab×1,=ab ........(iii)

product of a and b=ab .......(iv)

From (i) (ii) and (iii) (iv)

its proved lcm and hcf is equal to product of two numbers