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  4. 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

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Q. The number of ordered pairs of positive integers $\left(a , b\right),$ such that their Least Common Multiple is the given positive integer $7^{2}\times 11^{3}\times 19^{4},$ is equal to

NTA AbhyasNTA Abhyas 2020Permutations and Combinations

Solution:

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