LCM Fun...

Probability Level 5

The LCM of two numbers p p and q q is found out to be a 3 b 6 c 8 d 5 e 10 f 5 g 8 h 9 a^3b^6c^8d^5{e}^{10}f^5g^8h^9 . Where a,b,c,d,e,f,g,h are prime factors.

Find out the total numbers of ordered pair ( p , q ) ( p , q )

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The answer is 1269689421.

Aniket Sanghi by Aniket Sanghi , 21, India

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1 solution

Prakhar Bindal
Apr 6, 2016

Each of p and q will contain powers of a,b,c......,h.

For lcm we simply want Maximum power a particular prime factor in p and q be equal to power of the prime factor in there lcm .

For each prime factor we 2n+1 ways wherein n is power of prime factor in lcm

There fore answer is

7* 13* 17* 11* 21* 11 17 19 = 1269689421 :)

3 Helpful 0 Interesting 1 Brilliant 0 Confused

Right!....

And...prakhar ..what are the reference books you are told to prefer in fiitjee

Aniket Sanghi - 5 years, 2 months ago

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In physics we are being told HC Verma or DC Pandey. In maths no book is required. In chemistry they tell us solomon in organic, RC Mukherjee in physical and IDK about inorganic i am very bad at it

Prakhar Bindal - 5 years, 2 months ago

Done it same way :)

Gauri shankar Mishra - 5 years, 2 months ago

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Are you in Fiitjee

Aniket Sanghi - 5 years, 2 months ago

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Yes Fiitjee kanpur

Gauri shankar Mishra - 5 years, 2 months ago

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@Gauri shankar Mishra – What's your all india tests rank history

Aniket Sanghi - 5 years, 2 months ago

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@Aniket Sanghi – I am a pinnacle student WE only have phase tests :(

Gauri shankar Mishra - 5 years, 2 months ago

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@Gauri shankar Mishra – Here my friends in pinnacle give aiits......are you all being cheated

Aniket Sanghi - 5 years, 2 months ago

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@Aniket Sanghi – Yes we were being cheated .But presently we are going to center to study there . I hope that i will be giving the upcoming Aits

Gauri shankar Mishra - 5 years, 2 months ago

what about choosing the primes a,b,c,d,e,f,g,h? since they can be any prime, for every such combination of prime we shall have 126... numbers

Ajinkya Shivashankar - 4 years, 4 months ago

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