Lcm Of x cube y square and x y cube
Answers
Answer:
Required L.C.M = x³y³
Step-by-step explanation:
x³ = x ×x ×x
y² = y ×y
xy³ = x ×y ×y×y
Required L.C.M = x³y³
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Answer:
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.
or
Given that a = x²y³ = x × x × x × y x y
b = xy³ = x × y × y × y
HCF of a and b would be
= (x³, y², xy³) = x × y × y
HCF = xy²
HCF is the product of the smallest power of each common prime factor involved in the numbers.
LCM = x³y³
LCM is the lowest common factor of each power.
HCF × LCM
xy² × x³y³
ab = x⁴y⁵
Thus: ab = HCF ₓ LCM