# 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.

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