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 = 3¹ × 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 × v² × 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 × 5¹ × y × x

24y²x = 2 × 2 × 2 × 3 × y² × x

24y²x = 2^3 × 3¹ × y² × 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 × 3¹ × 5¹ × v

40u²v = 2 × 2 × 2 × 5 × u² × v

40u²v = 2³ × 5¹ × 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 × 3² × 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 × m² 

18nm² = 2 × 3² × n × m²

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

= 2² × 3² × 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 × x² × y² 

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 × x² 

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