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Find the L.C.M. of following algebraic terms,


2x,3x^(2),xy

2020. Find the L.C.M. of following algebraic terms,\newline2x,3x2,xy 2 x, 3 x^{2}, x y

Full solution

Q. 2020. Find the L.C.M. of following algebraic terms,\newline2x,3x2,xy 2 x, 3 x^{2}, x y
  1. Identify Variables Powers: Identify the highest powers of the variables in the given terms. 2x2x has xx to the power of 11, 3x23x^2 has xx to the power of 22, and xyxy has xx to the power of 11 and yy to the power of 11.
  2. Determine L.C.M. for xx: Determine the L.C.M. for the variable xx. The highest power of xx present in the terms is x2x^2.
  3. Determine L.C.M. for yy: Determine the L.C.M. for the variable yy. Since yy is only present in the term xyxy, its highest power is y1y^1.
  4. Combine Variable L.C.M.: Combine the L.C.M. of the variables.\newlineThe L.C.M. will be x2x^2 times y1y^1.
  5. Find Coefficient L.C.M.: Find the L.C.M. of the coefficients 22 and 33. The L.C.M. of 22 and 33 is 66.
  6. Write Final L.C.M.: Write the final L.C.M. by combining the L.C.M. of the coefficients with the L.C.M. of the variables.\newlineThe final L.C.M. is 6x2y6x^2y.

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