# FIND THE LEAST COMMON MULTIPLE OF MONOMIALS

Problem 1 :

12xy2, 39y3

Solution:

12xy2 = 2 × 2 × 3 × x × y2

12xy2 = 22 × 31 × ﻿x﻿ × y2

39y3 = 3 × 13 × y3

39y3 = 3× 131 × y3

By taking the highest power of each common factor, we get

= 22 × 3 × 13 × x × y3

LCM = 156xy3

Problem 2 :

33u, 9v2u

Solution:

33u = 3 × 11 × u

33u = 31 × 111 × u

9v2u = 3 × 3 × v2 × u

= 32 × v× u

By taking the highest power of each common factor, we get

= 32 × 11 × v2 × u

LCM = 99v2u

Problem 3 :

30yx, 24y2x

Solution:

30yx = 2 × 3 × 5 × y × x

30yx = 21 × 31 × 5× y × x

24y2x = 2 × 2 × 2 × 3 × y2 × x

24y2x = ﻿23﻿ × 31 × y× x

By taking the highest power of each common factor, we get

= 23 × 3 × 5 × y2 × x

LCM = 120y2x

Problem 4 :

30v, 40u2v

Solution:

30v = 2 × 3 × 5 × v

30v = 21 × 3× 51 × v

40u2v = 2 × 2 × 2 × 5 × u2 × v

40u2v = 23 × 5× u2 × v

By taking the highest power of each common factor, we get

= 23 × 3 × 5 × u2 × v

LCM = 120u2v

Problem 5 :

30ab2, 50b2

Solution:

30ab2 = 2 × 3 × 5 × a × b2

30ab2 = 21 × 31 × 51 × a × b2

50b2 = 2 × 5 × 5 × b2

50b2 = 21 × 52 × b2

By taking the highest power of each common factor, we get

= 2 × 3 × 52 × a × b2

LCM = 150ab2

Problem 6 :

30xy3, 20y3

Solution:

30xy3 = 2 × 3 × 5 × x × y3

30xy3 = 21 × 31 × 51 × x × y3

20y3 = 2 × 2 × 5 × y3

20y3 = 22 × 51 × y3

By taking the highest power of each common factor, we get

= 22 × 3 × 5 × x × y3

LCM = 60xy³

Problem 7 :

21b, 45ab

Solution:

21b = 3 × 7 × b

45ab = 3 × 3 × 5 × a × b

45ab = 32 × 5 × a × b

By taking the highest power of each common factor, we get

= 32 × 7 × 5 × a × b

LCM = 315ab

Problem 8 :

38x2, 18x

Solution:

38x2 = ﻿﻿2﻿﻿ × 19 × x2

18x = 2 × 3 × 3 × x

`18x = 2 × 3× x

By taking the highest power of each common factor, we get

= 2 × 32 × 19 × x2

LCM = 342x2

Problem 9 :

36m4, 9m2, 18nm2

Solution:

36m4 = 2 × 2 × 3 × 3 × m4

36m4 = 22 × 32 × m4

9m2 = 3 × 3 × m2

9m2 = 32 × m2

18nm2 = 2 × 3 × 3 × n × m

18nm2 = 2 × 32 × n × m2

By taking the highest power of each common factor, we get

= 22 × 3× n × m4

LCM = 36nm4

Problem 10 :

36m2n2, 30n2, 36n4

Solution:

36m2n2 = 2 × 2 × 3 × 3 × m2 × n2

36m2n2 = 22 × 32 × m2 × n2

30n2 = 2 × 3 × 5 × n2

30n2 = 21 × 31 × 51 × n2

36n4 = 2 × 2 × 3 × 3 × n4

36n4 = 22 × 32 × n4

By taking the highest power of each common factor, we get

= 22 × 32 × 5 × n4 × m2

LCM = 180n4m2

Problem 11 :

12xy, 8y2, 8x2

Solution:

12xy = 2 × 2 × 3 × x × y

12xy = 22 × 3 × x × y

8y2 = 2 × 2 × 2 × y2

8y2 = 23 × y2

8x2 = 2 × 2 × 2 × x2

8x2 = 23 × x2

By taking the highest power of each common factor, we get

= 23 × 3 × x× y

LCM = 24x2y2

Problem 12 :

32x2, 24yx2, 16yx2

Solution:

32x2 = 2 × 2 × 2 × 2 × 2 × x2

32x2 = 25 × x2

24yx2 = 2 × 2 × 2 × 3 × y × x2

24yx2 = 23 × 3 × y × x

16yx2 = 2 × 2 × 2 × 2 × x2

16yx2 = 24 × x2

By taking the highest power of each common factor, we get

= 25 × 3 × x2

LCM = 96yx2

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