1.
What is the least common multiple of 18 and 24?
Solution: 18 = 2×3×3 and 24 = 2×2×2×3. LCM = 2×2×2×3×3 = 72.
2.
Determine the greatest common factor of 65, 169, 52, and 26.
Solution: Factors common to all four numbers include 1 and 13. Therefore GCF = 13.
3.
Factor completely: \(-8x^3y^4-12x^2y\)
Solution: Factor out \(-4x^2y\): \(-4x^2y(2xy^3+3)\).
4.
Find the greatest common factor of \(5xy^2z^2\), \(15x^2yz^5\), and \(35x^5z^2\).
Solution: Common coefficient = 5, common variables = x and z². GCF = \(5xz^2\).
5.
What factor must \(-2x^2y^3\) be multiplied by to give a product of \(40x^3y^4\)?
Solution: \((40x^3y^4)\div(-2x^2y^3)=-20xy\).
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