# Worksheet on LCM

Practice the questions given in the worksheet on l.c.m. to find the least common multiple by listing their multiples, by common prime factors and by division method.

I. Find the L.C.M.  of the following by listing their multiples.

(i) 5, 10, 15

(ii) 4, 10, 12

(iii) 3, 9, 12

(iv) 2, 8, 10

(v) 7, 14, 21

(vi) 10, 20, 25

II. Find the first 3 common multiples of the given using a number line.

(i) 3 and 4

(ii) 5 and 6

III. Find the L.C.M.  of the following by finding common prime factors.

(i) 60, 75, 120

(ii) 48, 80, 112

(iii) 18, 54, 72

(iv) 10, 15, 25

(v) 20, 35, 45

(vi) 16, 24, 48

IV. Find the LCM of the given numbers by prime factorization method.

(i) 12 and 20

(ii) 36, 27 and 18

(iii) 32 and 48

(iv) 48, 64 and 120

(v) 56 and 72

(vi) 75, 150 and 275

V. Find the L.C.M. of the given numbers by division method.

(i) 20 and 44

(ii) 36, 24 and 40

(iii) 45 and 120

(iv) 84 and 90

(v) 10, 15 and 45

(vi)  70, 110, 150

(vii) 25, 30, 150

(viii) 36, 60, 120

(ix) 30, 150, 300

(x) 25, 45, 105

(xi) 21, 49, 63

VI. Solve the following:

(i) Find the lowest number which leaves 4 as remainder when divide by 9 and 12.

(ii) Find the lowest number which being increased by 3 is exactly divided by 8, 12 and 16.

(iii) Find the lowest number which is less by 5 to be divided by 15, 25 and 50 exactly.

(iv) Find the lowest number which is less by 2 to be divided by 56 and 98 exactly.

(v) Find the lowest number which is more by 7 to be divided by 20, 50 and 100 exactly.

(vi) The product of the L.C.M. and H.C.F. of two numbers is 80. If one of the numbers is 20, find the other number.

(vii) Find the lowest number which is less by 9 to be divided by 21, 35 and 49 exactly.

(viii) The product of two numbers is 192. If the H.C.F. of the numbers is 4, find their L.C.M.

(ix) The H.C.F. two numbers is 6 and their L.C.M. is 36. If one of the numbers is 18, find the other number.

(x) The product of the H.C.F. and L.C.M. of two numbers is 1050. Find the product of numbers.

(xi) The product of two numbers is 144. If the L.C.M. of these numbers is 12, find their H.C.F.

(xii) The product of two numbers is 169. If the L.C.M. of these numbers is 13, find their H.C.F.

Answers for the worksheet on lcm are given below.

I. (i) 30

(ii) 60

(iii) 36

(iv) 40

(v) 52

(vi) 100

II. (i) 12, 24, 36

(ii) 30, 60, 90

III. (i) 600

(ii) 1680

(iii) 216

(iv) 150

(v) 1260

(vi) 48

IV. (i) 60

(ii) 108

(iii) 96

(iv) 960

(v) 504

(vi) 1650

V. (i) 220

(ii) 360

(iii) 360

(iv) 1260

(v) 90

(vi) 11550

(vii) 150

(viii) 360

(ix) 300

(x) 1575

(xi) 441

VI. (i) 40

(ii) 45

(iii) 145

(iv) 390

(v) 107

(vi) 4

(vii) 726

(viii) 48

(ix) 12

(x) 1050

(xi) 12

(xii) 13