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.

Answers:

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

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8th Grade Math Practice

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