 # LCM of n numbers modulo 10^9+7

We all know that LCM of more than 2 numbers follows this property:

LCM(a,b,c)=LCM(a,LCM(b,c)) (can be proved easily : Useful link)

Now to find the LCM we can use LCM(a,b)* GCD(a,b)=a*b

I first tried to find the LCM of numbers using this and simply taking modulo at each step.

The problem with this method:

LCM(a,b,c)%mod = LCM(a,LCM(b,c))%mod. (This is a correct relation.)

What I was doing at each step:

LCM(a,LCM(b,c)%mod)%mod, this is wrong because

LCM(a,LCM(b,c)%mod)%mod != LCM(a,b,c)%mod (This was responsible for WA, I was assuming that these 2 values are equal)

Reference: http://stackoverflow.com/questions/16633449/calculate-lcm-of-n-numbers-modulo-1000000007

I guess this would have caused a lot of WA’s for a lot of users.

Then I tried to find the LCM using factorization and got AC using factorization.

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I used factorization to compute LCM.

and I used Python almost feels like cheating, lol

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Okay, Python can handle large numbers easily without any overflow problem and we can easily take the modulo at the last step.

I used Bigint library for c++ … no worries :-p

This question could have also been done with great ease in JAVA, using BigInteger.