Worksheet on H.C.F. and L.C.M. of Monomials

Practice the questions given in the worksheet on H.C.F. and L.C.M. of monomials. The questions are based on finding the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of two or more monomials.

1. Find the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of the two monomials:

(i) m2n and mn2

(ii) a2bc3 and ab2cd

(iii) 15p2q3 and 12p3q

(iv) 13x2yz and 39x3yz2

(v) 17abc2 and 51a2b

(vi) 15p3q3r and 25pq3r2

(vii) 17a2b4k2 and 51a4k4

(viii) 72a2x3y4 and 108a3x2y5

2. Find the H.C.F. and L.C.M. of the following three monomials:

(i) 2xyz, 3xz and 4xyz 

(ii) 2ab, 4bc and 6abc

(iii) 9pqr, 3q2r and pqr

(iv) 3mn2, 15m2n3 and 21m3n2

(v) 11xyz3, 33x2y2z and 99xyz

(vi) -4m5, -16m3n and -20m2n2

(vii) x3yz, 4xy3 and 8z2

(viii) 3xy, 2yz and 5xyz

(ix) 20x2y3, 32x3y2z and 8xz3

(x) 5ab, 9b2c and 15ac3

(xi) a3b2, b2c4 and a3b5c4

(xii) 15x3y4, 20k2x2y3 and 30kx3

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


1. (i) H.C.F. = mn and L.C.M. = m2n2

(ii) H.C.F. = abc and L.C.M. = a2b2c3d

(iii) H.C.F. = 3p2q and L.C.M. = 60p3q3

(iv) H.C.F. = 13x2yz and L.C.M. = 39x3yz2

(v) H.C.F. = 17ab and L.C.M. = 51a2bc2

(vi) H.C.F. = 5pq3r and L.C.M. = 75p3q3r2

(vii) H.C.F. = 17a2k2 and L.C.M. = 51a4b4k4

(viii) H.C.F. = 36a2x2y4 and L.C.M. = 216a3x3y5

2. (i) H.C.F. = xz and L.C.M. = 12xyz

(ii) H.C.F. = 2b and L.C.M. = 12abc

(iii) H.C.F. = qr and L.C.M. = 9pq2r

(iv) H.C.F. = 3mn2 and L.C.M. = 105m3n3

(v) H.C.F. = 11xyz and L.C.M. = 99x2y2z3

(vi) H.C.F. = -4m2 and L.C.M. = -80m5n2

(vii) H.C.F. = 1 and L.C.M. = 8x3y3z2

(viii) H.C.F. = y and L.C.M. = 30xyz

(ix) H.C.F. = 4x and L.C.M. = 160x3y3z3

(x) H.C.F. = 1 and L.C.M. = 45ab2c3

(xi) H.C.F. = b2 and L.C.M. = a3b5c4

(xii) H.C.F. = 5x2 and L.C.M. = 60k2x3y4

Math Homework Sheets

8th Grade Math Practice

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