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Question
If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.
Options
xy
xy2
x3y3
x2y2
Solution
If two positive integers a and b are written as a = x3y2 and b = xy3, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is xy2.
Explanation:
Given,
a = x3y2
b = xy3
∴ a × b = x3y2 × xy3
= x4y5
a = x3y2 = x × x × x × y × y
b = xy3 = x × y × y × y
LCM = x3y3
Product ÷ LCM
`(x^4y^5)/(x^3y^3)` = xy2
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