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If two positive integers a and b are written as a=x^3y^2 and b=xy^3,where X,y are prime numbers then LCM (a,b) is.?
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If two positive integers a and b are written as a=x^3y^2 and b=xy^3,wh...
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If two positive integers a and b are written as a=x^3y^2 and b=xy^3,wh...
Given Information:

Two positive integers, a and b, are written as:

a = x^3y^2

b = xy^3

Where x and y are prime numbers.


Finding the LCM:

To find the least common multiple (LCM) of a and b, we need to determine the highest power of each prime factor that appears in either a or b. We can then multiply these prime factors together to find the LCM.


Prime Factors of a:

The prime factors of a are x and y.

a = x^3y^2


Prime Factors of b:

The prime factors of b are x and y.

b = xy^3


Highest Power of Each Prime Factor:

For the prime factor x, the highest power that appears in either a or b is x^3.

For the prime factor y, the highest power that appears in either a or b is y^3.


LCM Calculation:

To find the LCM, we multiply the highest powers of each prime factor:

LCM(a, b) = x^3 * y^3


Final Answer:

The LCM of a and b is x^3 * y^3.
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