The number of ordered pairs of positive integers (a , b), such that their Least Common Multiple is the given positive integer 72× 113× 194, is equal to

Question

The number of ordered pairs of positive integers (a , b), such that their Least Common Multiple is the given positive integer 72× 113× 194, is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-sobmqqu4kxnm.png" /> Required number of ordered pairs =(2 × 2 + 1)(2 × 3 + 1)(2 × 4 + 1) =5× 7× 9=315

Q. The number of ordered pairs of positive integers $(a, b),$ such that their Least Common Multiple is the given positive integer $7^{2} \times 1 1^{3} \times 1 9^{4},$ is equal to

Required number of ordered pairs
$= (2 \times 2 + 1) (2 \times 3 + 1) (2 \times 4 + 1)$
$= 5 \times 7 \times 9 = 315$

Q. The number of ordered pairs of positive integers (a,b), such that their Least Common Multiple is the given positive integer 72×113×194, is equal to

Required number of ordered pairs =(2×2+1)(2×3+1)(2×4+1) =5×7×9=315

Q. The number of ordered pairs of positive integers $(a, b),$ such that their Least Common Multiple is the given positive integer $7^{2} \times 1 1^{3} \times 1 9^{4},$ is equal to

Required number of ordered pairs
$= (2 \times 2 + 1) (2 \times 3 + 1) (2 \times 4 + 1)$
$= 5 \times 7 \times 9 = 315$