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Lowest Common Multiple of Monomials | Solved Example Questions

The lowest common multiple of monomials or L.C.M of monomials is the least occurred term in the monomials. Find the numerical coefficients LCM, literal coefficients LCM, and multiply them to get the result. You can check out the following sections to get the simple steps to calculate the least common multiple of two or monomials. Also, find the solved example questions for a better understanding of the concept.

How to Find L.C.M of Monomials?

Learn about how to get the lowest common multiple of monomials by using the steps mentioned below. Follow these easy to use steps to get the answer easily.

  • Find the factors of given monomials numerical coefficients.
  • And get the least common multiple from those factors.
  • Get the highest power of each variable from the monomials.
  • Calculate the LCM of literal coefficients.
  • Multiply the LCM of numerical coefficients and literal coefficients.

Examples on Lowest Common Multiple of Monomials

Example 1:

Find the LCM of 12x²y³z and 18xy²z.

Solution:

The L.C.M of Numerical coefficients = The L.C.M. of 12, 18.

Since, 12 = 2 * 2 * 3 and 18 = 2 * 3 * 3

Therefore, the LCM of 12, 18 is 2 * 2 * 3 * 3= 36

The L.C.M. of literal coefficients = The L.C.M. of x²y³z, xy²z = x²y³z

Since in x²y³z and xy²z

The highest power of x is 2.

The highest power of y is 3.

The highest power of z is 1.

Therefore, the L.C.M. of x²y³z, xy²z = x²y³z

Thus, the L.C.M. of 12x²y³z and 18xy²z = The L.C.M. of numerical coefficients × The L.C.M. of literal coefficients

= 36 * x²y³z

= 36x²y³z

Example 2:

Find the L.C.M of 26p⁴q²r³ and 16p³q²r².

Solution:

The L.C.M. of numerical coefficients = The L.C.M. of 26, 16

Since, 26 = 2 * 13, 16 = 2 * 2 * 2 * 2

Therefore, the L.C.M. of 26, 16 is 2 * 13 * 8 = 206.

The L.C.M. of literal coefficients = The L.C.M. of p⁴q²r³, p³q²r²

Since in p⁴q²r³ and p³q²r²,

The highest power of p is 4.

The highest power of q is 2.

The highest power of r is 3.

Therefore, the L.C.M. of p⁴q²r³ and p³q²r² = p⁴q²r³

Thus, the L.C.M of 26p⁴q²r³ and 16p³q²r² = The L.C.M. of numerical coefficients × The L.C.M. of literal coefficients

= 206 * p⁴q²r³

= 206p⁴q²r³

Example 3:

Find the LCM of 24y³x, 40x³y.

Solution:

The L.C.M. of numerical coefficients = The L.C.M. of 24 and 40.

Since, 24 = 2 * 2 * 2 * 3 and 40 = 2 * 2 * 2 * 5

Therefore, the L.C.M. of 24 and 40 is = 2 * 2 * 2 * 3 * 5 = 120

The L.C.M. of literal coefficients = The L.C.M. of y³x and x³y = x³y³

Since, in y³x and x³y,

The highest power of x is 3.

The highest power of y is 3.

Therefore, the L.C.M. of y³x and x³y = x³y³.

Thus, the L.C.M. of 24y³x, 40x³y

= The L.C.M. of numerical coefficients × The L.C.M. of literal coefficients

= 120 × (x³y³)

= 120x³y³.

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