Multiple choice general knowledge math & puzzles

Find the G.C.D of 12x^2y^3z^2, 18x^3y^2z^4, and 24xy^4z^3

  1. 6x^3y^4z^3

  2. 24xy^2z^2

  3. 18x^2y^2z^3

  4. 6xy^2z^2

  5. 6x^3y^4z^4
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find GCD, take the lowest power of each common variable: for coefficient, GCD of 12, 18, 24 is 6. For x: lowest power is x (x^1 from third term). For y: lowest power is y^2 (from second term). For z: lowest power is z^2 (from first term). So GCD = 6xy^2z^2, which is option D.

AI explanation

To find the GCD of 12x²y³z², 18x³y²z⁴, and 24xy⁴z³: first take the GCD of the coefficients 12, 18, 24, which is 6. Then for each variable, take the lowest exponent appearing across all three terms: x appears as x², x³, x¹ → minimum is x¹; y appears as y³, y², y⁴ → minimum is y²; z appears as z², z⁴, z³ → minimum is z². Combining these gives 6xy²z², matching the correct answer. The other options either use the wrong coefficient (24 or 18, which are not common to all three) or the wrong exponents (using maximum instead of minimum, as in 6x³y⁴z³/z⁴).

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