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If two positive integers a nad b are written as a = x^4 y^2 and b = x^2y^3 , where x and y are prime numbers, then LCM (a,b)?
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If two positive integers a nad b are written as a = x^4 y^2 and b = x^...
Given:
Two positive integers a and b are written as a = x^4y^2 and b = x^2y^3, where x and y are prime numbers.

To find:
The least common multiple (LCM) of a and b.

Solution:
To find the LCM of two numbers, we need to find the product of the highest powers of all the prime factors that appear in both numbers.
Here, a and b are represented as powers of prime numbers x and y. Let's analyze the prime factors of a and b separately.

Prime factors of a:
a = x^4y^2
The prime factors of a are x and y.
The highest power of x in a is x^4.
The highest power of y in a is y^2.

Prime factors of b:
b = x^2y^3
The prime factors of b are x and y.
The highest power of x in b is x^2.
The highest power of y in b is y^3.

LCM:
To find the LCM, we take the highest power of each prime factor that appears in a and b.
The LCM of a and b will be the product of these highest powers.

Factors in a:
x^4 and y^2

Factors in b:
x^2 and y^3

Highest powers for x and y:
The highest power of x is x^4 (from a).
The highest power of y is y^3 (from b).

LCM(a,b):
LCM(a,b) = x^4 * y^3

Now, let's simplify the expression for the LCM:

LCM(a,b) = x^4 * y^3
Community Answer
If two positive integers a nad b are written as a = x^4 y^2 and b = x^...
X^4 y^3
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