CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If p and q are positive integers such that L.C.M of p & q is 360 and the total possible number of ordered pairs (p,q) is N, then the remainder when N is divided by 6, is

Open in App
Solution

360=23×32×5
Let p=2a×3b×5c, q=2d×3e×5f
pq=360=2a+d 3b+e 5c+f
a+d=3 , a,d0
b+e=2 , b,e0
c+f=1 , c,f0
No. of solutions of a+d=3 is 3+21C21=4
No. of solutions of b+e=3 is 2+21C21=3
No. of solutions of c+f=3 is 1+21C21=2
Total possibilities =4×3×2=24=N
N6=246=4
Remainder =0.
Hence, the answer is 0.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Compound Statement
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon