Lowest Common Factor of Monomials

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:

1. Find the L.C.M. of 24x³y²z and 30x²y³z⁴.

Solution:

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

Since, 24 = 2 × 2 × 2 × 3 = 2³ × 3¹ and 30 = 2 × 3 × 5 = 2¹ × 3¹ × 5¹

Therefore, the L.C.M. of 24 and 30 is 2³ × 3¹ × 5¹ = 2 × 2 × 2 × 3 × 5 = 120

The L.C.M. of literal coefficients = The L.C.M. of x³y²z and x²y³z⁴ = x³y³z⁴

Since, in x³y²z and x²y³z⁴,

The highest power of x is x³.

The highest power of y is y³.

The highest power of z is z⁴.

Therefore, the L.C.M. of x³y²z and x²y³z⁴ = x³y³z⁴.

Thus, the L.C.M. of 24x³y²z and 30x²y³z⁴

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

= 120 × (x³y³z⁴)

= 120x³y³z⁴.



2. Find the L.C.M. of 18x²y²z³ and 16xy²z².

Solution:

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

Since, 18 = 2 × 3 × 3 = 2¹ × 3² and 16 = 2 × 2 × 2 × 2 = 2⁴

Therefore, the L.C.M. of 18 and 16 is 2⁴ × 3² = 2 × 2 × 2 × 2 × 3 × 3 = 144

The L.C.M. of literal coefficients = The L.C.M. of x²y²z³ and xy²z² = x²y²z³

Since, in x²y²z³ and xy²z²,

The highest power of x is x².

The highest power of y is y².

The highest power of z is z³.

Therefore, the L.C.M. of x²y²z³ and xy²z² = x²y²z³.

Thus, the L.C.M. of 18x²y²z³ and 16xy²z²

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

= 144 × (x²y²z³)

= 144x²y²z³.

8th Grade Math Practice

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