SOLUTION: What is the least common multiple of 3w^4x^6y and 16w^3x^6

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Question 348066: What is the least common multiple of 3w^4x^6y and 16w^3x^6

Found 2 solutions by Jk22, Theo:
Answer by Jk22(389) (Show Source):
You can put this solution on YOUR website!
LCM(3w^4x^6y and 16w^3x^6)=3*2^4*(w^4*x^6*y)

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
A common factor of both expressions would probably be w^3*x^6

Your first expression would be equivalent to (w^3*x^6)*(3*w*y) = 3*w^4*x^6*y

Your second expression would be equivalent to (w^3*x^6)*(16) = 16*w^3*x^6

To confirm this is true, then use some random numbers for w and x and y and see if the relationships are equivalent.

Let w = 3 and x = 4 and y = 5.

(w^3*x^6) = 110592

(w^3*x^6) * (3*w*y) becomes 110592 * 45 = 4976640

(w^3*x^6) * (16) becomes 110592 * 16 = 1769472

3*w^4*x^6*y = 4976640 which makes it equivalent to (w^3*x^6) * (3*w*y)

16*w^3*x^6 = 1769472 which makes it equivalent to (w^3*x^6) * (16)

The common multiple appears to be:

w^3*x^6

I couldn't find any other common multiples in these equations.

The applicable basic laws of multiplication and exponentiation appear to be:

a*(b*c) = (a*b)*c

a*b = b*a

a^b * a^c = a^(b+c)