jee-advanced 2006 Q8

jee-advanced · India Number Theory GCD, LCM, and Coprimality

8. If $r , s , t$ are prime numbers and $p , q$ are the positive integers such that the LCM of $p , q$ is $r ^ { 2 } t ^ { 4 } s ^ { 2 }$, then the number of ordered pair ( $p , q$ ) is
(A) 252
(B) 254
(C) 225
(D) 224
Sol. (C) Required number of ordered pair (p,q) is $( 2 \times 3 - 1 ) ( 2 \times 5 - 1 ) ( 2 \times 3 - 1 ) = 225$.

If $r , s , t$ are prime numbers and $p , q$ are the positive integers such that the LCM of $p , q$ is $r ^ { 2 } t ^ { 4 } s ^ { 2 }$, then the number of ordered pair ( $p , q$ ) is

8. If $r , s , t$ are prime numbers and $p , q$ are the positive integers such that the LCM of $p , q$ is $r ^ { 2 } t ^ { 4 } s ^ { 2 }$, then the number of ordered pair ( $p , q$ ) is\\
(A) 252\\
(B) 254\\
(C) 225\\
(D) 224

Sol. (C)\\
Required number of ordered pair (p,q) is $( 2 \times 3 - 1 ) ( 2 \times 5 - 1 ) ( 2 \times 3 - 1 ) = 225$.\\

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