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) 16, 48 and 64
(ii) 21, 14 and 7
(iii) 24, 16 and 12
(iv) 45 and 35
(v) 27 and 15
(vi) 2, 8 and 9
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. Multiple Choice Questions (MCQ) on Prime Factorization:
Tick (✔) the correct option.
(i) The LCM of 46 and 276 is
(a) 46; (b) 244; (c) 36; (d) 28
(ii) If p and q are co-primes, then their LCM is
(a) 1; (b) pq; (c) \(\frac{p}{q}\); (d) \(\frac{1}{2}\)pq
VII. Use the prime factorization method to find the LCM of the following groups of numbers.
(i) 16, 32 and 64
(ii) 7, 14 and 21
(iii) 12, 16 and 24
(iv) 35 and 45
(v) 15 and 27
(vi) 2, 8 and 9
VIII. Find the LCM of the group of numbers given below:
(i) 7, 14
(ii) 10, 14
(iii) 14, 15
(iv) 11, 13
(v) 4 ,27, 36
(vi) 22, 14, 126
(vii) 50, 100, 200
(viii) 24, 36, 40
(ix) 20, 24, 45
(x) 112, 140, 168
(xi) 144, 180, 384
(xii) 660, 420, 240
IX. 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.
(xiii) Show that 147 is the multiple of 3 and 7, but not of 13.
(xiv) What is the LCM of two consecutive numbers?
(xv) Can the LCM of a group of numbers be less than any of these numbers?
(xvi) Can the LCM of a group of numbers be equal to any of these numbers?
(xvii) Can the LCM of a group of numbers be more than any of these numbers?
Answers for the worksheet on lcm are given below.
Answers:
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) (a) 46
(ii) (b) pq
VII. (i) LCM of 16, 32 and 64 is 64
(ii) LCM of 7, 14 and 21 is 42
(iii) LCM of 12, 16 and 24 is 48
(iv) LCM of 35 and 45 is 315
(v) LCM of 15 and 27 is 135
(vi) LCM of 2, 8 and 9 is 72
VIII. (i) LCM of 7, 14 is 14
(ii) LCM of 10, 14 is 70
(iii) LCM of 14, 15 is 210
(iv) LCM of 11, 13 is 143
(v) LCM of 4 ,27, 36 is 108
(vi) LCM of 22, 14, 126 is 1,386
(vii) LCM of 50, 100, 200 is 200
(viii) LCM of 24, 36, 40 is 360
(ix) LCM of 20, 24, 45 is 360
(x) LCM of 112, 140, 168 is 1,680
(xi) LCM of 144, 180, 384 is 5,760
(xii) LCM of 660, 420, 240 is 18,480
IX. (i) 40
(ii) 45
(iii) 145
(iv) 390
(v) 107
(vi) 4
(vii) 726
(viii) 48
(ix) 12
(x) 1050
(xi) 12
(xii) 13
(xiii)
(xiv) multiplication of two numbers
(xv) No
(xvi) Yes
(xvii) Yes
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