Two positive integers a and b can be written as a = x³y² and b = xy³, where x and y are prime numbers. Find HCF(a,b) and LCM(a,b).
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Answers
Step-by-step explanation:
Given :-
Two positive integers a and b can be written as a = x³y² and b = xy³, where x and y are prime numbers.
To find :-
Find HCF(a,b) and LCM(a,b). ?
Solution :-
Given that
Two positive integers a and b can be written as a = x³y² and b = xy³, where x and y are prime numbers
a = x³y² = x³ × y²
b = xy³ = x × y³
HCF of two numbers is the product of the smallest power of each common prime factors of the numbers
=> HCF(a,b) = x × y²
HCF (a,b) = xy²
LCM is the product of the greatest power of each prime factors of the numbers
=> LCM(a,b) = x³ × y³
LCM (a,b) = x³y³
Answer :-
HCF (a,b) = xy²
LCM (a,b) = x³y³
Used formulae:-
→ LCM is the product of the greatest power of each prime factors of the numbers
→ HCF of two numbers is the product of the smallest power of each common prime factors of the numbers