Two positive integers have HCF $6$ and LCM $90$. One integer is $18$. Find the other integer a

Question

Two positive integers have HCF $6$ and LCM $90$. One integer is $18$. Find the other integer and check your answer. Let $$ A=2^a\times3^2,\qquad B=2^3\times3^b, $$ where $a,b$ are positive integers. Given $$ \operatorname{HCF}(A,B)=2^2\times3,\qquad \operatorname{LCM}(A,B)=2^3\times3^2, $$ find $a$ and $b$.

Accepted Answer

(a) $n=30$ (b) $ a=2, b=1$

Primes, HCF and LCM

Primes, HCF and LCM

Solution:

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