Q6 Ans:B How 6 The number of ordered pairs of positive integers (a, b) such that - Maths -

Question

Q6
Ans:B
How?

6 The number of ordered pairs of positive integers (a,
b) such that their least common multiple in the given
positive integer 72 × 113 ×
194 is
(A) 215
(B) 315
(C) 415
(D) 195

Zuhaib Ul Zamann · Accepted Answer

Dear student,
Let a=7α1×11β1×19γ1and b=7α2×11β2×19γ2Now as 72×113×194 is LCM we must havemaxα1,α2=2 maxβ1,β2=3 and maxγ1,γ2=4So if α1=2 then α2=0,1,2Similarly if α2=2 then  α1=0,1,2Hence a total of 2×2+1 waysSimilarly maxβ1,β2=3  in total of 2×3+1 waysand  maxγ1,γ2=4 in total of 2×4+1 waysHence total number of ordered pairs =5×7×9=315Regards

Q6. Ans:B How? 6. The number of ordered pairs of positive integers (a, b) such that their least common multiple in the given positive integer 72 × 113 × 194 is (A) 215 (B) 315 (C) 415 (D) 195

Q6.
Ans:B
How?

6. The number of ordered pairs of positive integers (a, b) such that their least common multiple in the given positive integer 7² × 11³ × 19⁴ is
(A) 215
(B) 315
(C) 415
(D) 195