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) m
^{2}n and mn
^{2}
(ii) a
^{2}bc
^{3} and ab
^{2}cd
(iii) 15p
^{2}q
^{3} and 12p
^{3}q
(iv) 13x
^{2}yz and 39x
^{3}yz
^{2}
(v) 17abc
^{2} and 51a
^{2}b
(vi) 15p
^{3}q
^{3}r and 25pq
^{3}r
^{2}
(vii) 17a
^{2}b
^{4}k
^{2} and 51a
^{4}k
^{4}
(viii) 72a
^{2}x
^{3}y
^{4} and 108a
^{3}x
^{2}y
^{5}
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, 3q
^{2}r and pqr
(iv) 3mn
^{2}, 15m
^{2}n
^{3} and 21m
^{3}n
^{2}
(v) 11xyz
^{3}, 33x
^{2}y
^{2}z and 99xyz
(vi) -4m
^{5}, -16m
^{3}n and -20m
^{2}n
^{2}
(vii) x
^{3}yz, 4xy
^{3} and 8z
^{2}
(viii) 3xy, 2yz and 5xyz
(ix) 20x
^{2}y
^{3}, 32x
^{3}y
^{2}z and 8xz
^{3}
(x) 5ab, 9b
^{2}c and 15ac
^{3}
(xi) a
^{3}b
^{2}, b
^{2}c
^{4} and a
^{3}b
^{5}c
^{4}
(xii) 15x
^{3}y
^{4}, 20k
^{2}x
^{2}y
^{3} and 30kx
^{3}
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. = m
^{2}n
^{2}
(ii) H.C.F. = abc and L.C.M. = a
^{2}b
^{2}c
^{3}d
(iii) H.C.F. = 3p
^{2}q and L.C.M. = 60p
^{3}q
^{3}
(iv) H.C.F. = 13x
^{2}yz and L.C.M. = 39x
^{3}yz
^{2}
(v) H.C.F. = 17ab and L.C.M. = 51a
^{2}bc
^{2}
(vi) H.C.F. = 5pq
^{3}r and L.C.M. = 75p
^{3}q
^{3}r
^{2}
(vii) H.C.F. = 17a
^{2}k
^{2} and L.C.M. = 51a
^{4}b
^{4}k
^{4}
(viii) H.C.F. = 36a
^{2}x
^{2}y
^{4} and L.C.M. = 216a
^{3}x
^{3}y
^{5}
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. = 9pq
^{2}r
(iv) H.C.F. = 3mn
^{2} and L.C.M. = 105m
^{3}n
^{3}
(v) H.C.F. = 11xyz and L.C.M. = 99x
^{2}y
^{2}z
^{3}
(vi) H.C.F. = -4m
^{2} and L.C.M. = -80m
^{5}n
^{2}
(vii) H.C.F. = 1 and L.C.M. = 8x
^{3}y
^{3}z
^{2}
(viii) H.C.F. = y and L.C.M. = 30xyz
(ix) H.C.F. = 4x and L.C.M. = 160x
^{3}y
^{3}z
^{3}
(x) H.C.F. = 1 and L.C.M. = 45ab
^{2}c
^{3}
(xi) H.C.F. = b
^{2} and L.C.M. = a
^{3}b
^{5}c
^{4}
(xii) H.C.F. = 5x
^{2} and L.C.M. = 60k
^{2}x
^{3}y
^{4}
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Math Homework Sheets
8th Grade Math Practice
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