Question

Q. If two positive integer a and b are written as a=x^{​​​​​​3}​​y​​^{​​​​2} and b=xy^{​​​​​3} ; x and y are prime numbers, then find the HCF (a,b).

Answer 1

When getting LCM using indices, we get the highest indices of the two and when getting HCF we get the lowest power of the two unknowns.

a = x³y² , b= xy³

LCM

Comparing indices of x and y in numbers a and b.

a : x's index is 3 whereas y's index is 2

b: x's index is 1 and y's index is 3.

Comparing the two: the highest index of x is 3 and the highest index of y is 3.

LCM = The highest indices of the unknowns (x and y)

LCM =x³y³

HCF = The lowest indices of x and y

The lowest index of x is 1 and the lowest index of y is 2.

HCF = xy²

a