How to find the lowest common multiple of monomials?

To find the lowest common multiple (L.C.M.) of two or more monomials is the product of the L.C.M. of their numerical coefficients and the L.C.M. of their literal coefficients.

Note: The L.C.M. of literal coefficients is each literal contained in the expression with the highest power.

Solved examples to find lowest common multiple of monomials:

The L.C.M. of numerical coefficients = The L.C.M. of 24 and 30.

Since, 24 = 2 × 2 × 2 × 3 = 2

Therefore, the L.C.M. of 24 and 30 is 2

The L.C.M. of literal coefficients = The L.C.M. of x

Since, in x

The highest power of x is x

The highest power of y is y

The highest power of z is z

Therefore, the L.C.M. of x

Thus, the L.C.M. of 24x

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

= 120 × (x

= 120x

The L.C.M. of numerical coefficients = The L.C.M. of 18 and 16.

Since, 18 = 2 × 3 × 3 = 2

Therefore, the L.C.M. of 18 and 16 is 2

The L.C.M. of literal coefficients = The L.C.M. of x

Since, in x

The highest power of x is x

The highest power of y is y

The highest power of z is z

Therefore, the L.C.M. of x

Thus, the L.C.M. of 18x

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

= 144 × (x

= 144x

**8th Grade Math Practice**

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