# Worksheet on L.C.M. of Monomials

Practice the worksheet on L.C.M. of monomials. The questions are based on finding the lowest common multiple of two or more monomials. We know, the lowest common multiple (L.C.M.) of two or more monomials is the monomial of lowest dimensions which is divisible by each of them without remainder.

For example: The lowest common multiple of m6, m5, m4, m3, m2 is m6.

If the monomials have numerical coefficients, find by Arithmetic their least common measure, and prefix it as a coefficient to the algebraical lowest common multiple.

For example: The lowest common multiple of 14m4a3b, 21m2a4b and 35m3ab4 is 210m4a4b4; for it consists of the product of:

(i) the least common measure of the numerical coefficients;

(ii) the lowest power of each letter which is divisible by every power of that letter occurring in the given expressions.

1. Find the lowest common multiple (L.C.M.) of the two monomials:

(i) xyz and 2x2

(ii) a3b2 and abc

(iii) 3a2bc and 4a3b3

(iv) 5x2yz3 and 4xy2z

(v) 3x4y2z3 and 5x2y3z5

(vi) 12mn and 8pq

2. Find the lowest common multiple (L.C.M.) of the three monomials:

(i) xz, yz and xy

(ii) x2z, yz2 and y2z

(iii) 2xy, 3xy and 4xz

(iv) 2a, 3b and 4c

(v) 3a2, 4b2 and 3c2

(vi) 7x2, 2xy and 3y3

(vii) x2yz, xy2z and xyz2

(viii) 5x2z, 6y2z and 3yz2

(ix) 2m2n3, 3mn and 4m3n4

(x) 7m4n, 8mn5 and 2m3n3

(xi) 35x2yz3, 42x3y2z and 30xy3z2

(xii) 66p4q2r3, 44p3q4r2 and 24p2q3r4



Answers for the worksheet on L.C.M. of monomials are given below to check the exact answers of the above questions.

1. (i) 2x2yz

(ii) a3b2c

(iii) 12a3b3c

(iv) 20x2y2z3

(v) 15x4y3z5

(vi) 24mnpq

2. (i) xyz

(ii) x2y2z2

(iii) 12xyz

(iv) 12abc

(v) 12a2b2c2

(vi) 42x2y3

(vii) x2y2z2

(viii) 30x2y2z2

(ix) 12m3n4

(x) 56m4n5

(xi) 210x3y3z3

(xii) 264p4q4r4