# Worksheet on H.C.F. and L.C.M. of Polynomials

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

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

(i) a3 + 2a2 – 3a and 2a3 + 5a2 – 3a

(ii) 4u2 – 9v2 and 2u2 – 3uv

(iii) (4u2 – 25v2) and (6u2 + 15uv)

(iv) m2 + 9m + 20 and m2 + 13m + 36

(v) k2 + 2k – 15 and k2 + (26/5)k + 1

2. Find the highest common factor (H.C.F.) and lowest common multiple (L.C.M.) of the three polynomials:

(i) 3m2 – 7m2n + 5mn2 – n3, m2n + 3mn2 – 3m3 – n3 and 3m3 + 5m2n + mn2 – n3

(ii) a2 – 5a + 6, a2 – 4 and a3 – 3a - 2

(iii) t2 + 3t – 4, t2 + 5t + 4 and t2 – 1

(iv) p2 + 8p + 12, p2 + 2p – 24 and p2 + 15p + 54

(v) d2 + 15d + 56, d2 + 5d – 24 and d2 + 8d

3. Find the lowest common multiple of xy(k2 + 1) + k(x2 + y2) and xy(k2 – 1) + k(x2 – y2).

4. Find the L.C.M. of pq – np, pq – mq, q2 – 3nq + 2n2, pq – 2np – mq + 2mn and pq – np – mq + mn.

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

1. (i) H.C.F = a(a + 3)

L.C.M. = a(a – 1) (a + 3) (2a – 1)

(ii) H.C.F = 2u – 3v

L.C.M. = u(2u + 3v)(2u – 3v)

(iii) H.C.F = 2u + 5v

L.C.M. = 3u(2u + 5v) (2u – 5v)

(iv) H.C.F = m + 4

L.C.M. = (m + 4) (m + 5) (m + 9)

(v) H.C.F = k + 5

L.C.M. = (k + 5) (k – 3) (k + 1/5)

2. (i) H.C.F = 3m - n

L.C.M. = (3m – n) (m + n)2 ( - n)2

(ii) H.C.F = a - 2

L.C.M. = (a + 1)2 (a + 2) (a – 2) (a – 3)

(iii) H.C.F = 1

L.C.M. = (t + 4) (t + 1) (t - 1)

(iv) H.C.F = p + 6

L.C.M. = (p + 2) (p + 6) (p + 9) (p - 4)

(v) H.C.F = d + 8

L.C.M. = d(d + 8) (d + 7) (d - 3)

3. (kx + y) (kx – y) (ky + x)

4. pq(p – m) (q – n) (q – 2n)