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.

Answers:

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

Math Homework Sheets

8th Grade Math Practice

From Worksheet on L.C.M. of Monomials to HOME PAGE