Question

If two positive integers a and b are written as a=x^3y^2 and b=xy^2. Find the hcf and lcm of a and b
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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

ab = x³y²(xy³) = x⁴y⁵

HCF × LCM = x³y³(xy²) = x⁴y⁵

Thus ab = LCM × HCF.