HOW TO FIND LEAST COMMON MULTIPLE ALGEBRAIC TERMS

Problem 1 :

18, 6v

Solution:

18, 6v

18 = 3² × 2

6v = 2 × 3 × v

Least common multiple of 18, 6 is 3² ⋅ 2 

= 18v

So, the required LCM is 18v.

Problem 2 :

3x², 10

Solution:

3x², 10

3x² = 3 × x × x

10 = 2 × 5

Least common multiple of 3, 10 is 2 ⋅ 3 ⋅ 5

= 30x²

So, the required LCM is 30x².

Problem 3 :

30ab², 50b²

Solution:

30ab² = 3 × 2 × 5 × a × b × b

50b² = 5² × 2 × b × b

Least common multiple of 30, 50 is 5² ⋅ 2 ⋅ 3

= 150ab²

So, the required LCM is 150ab².

Problem 4 :

30xy³, 20y³

Solution:

30xy³ = 2 × 3 × 5 × x × y × y × y

20y³ = 2² × 5 × y × y × y

Comparing y terms (LCM) is y³

Least common multiple of 30, 20 is 2² ⋅ 5 ⋅ 3

= 60xy³

Problem 5 :

20y, 14y²

Solution:

20y = 2² × 5 × y

14y² = 2 × 7 × y × y

Least common multiple of 20, 14 is 2² ⋅ 5 ⋅ 7

= 140y²

Problem 6 :

25x², 25y

Solution:

25x² = 5² × x × x

25y = 5² × y

LCM = 5² × x²y

= 25x²y

Problem 7 :

21b, 45ab

Solution:

21b = 7 × 3 × b

45ab = 3² × 5 × a × b

Least common multiple of 21, 45 is 3² ⋅ 5 ⋅ 7

= 315ab

Problem 8 :

38x², 18x

Solution:

38x² = 2 × 19 × x × x

18x = 3² × 2 × x

Least common multiple of 38, 18 is 3² ⋅ 2 ⋅ 19

= 342x²

Problem 9 :

32u², 14v²

Solution:

32u² = 2² × 2² × 2 × u × u

14v² = 2 × 7 × v × v

Least common multiple of 32, 14 is 2² ⋅ 2² ⋅ 2 ⋅ 7

= 224u²v²

Problem 10 :

18m², 24nm

Solution:

18m² = 3² × 2 × m × m

24nm = 2² × 2 × 3 × n × m

Least common multiple of 18, 24 is 3² ⋅ 2² ⋅ 2 

= 72m²n

Problem 11 :

36m⁴, 9m², 18nm²

Solution:

36m⁴ = 2² × 3² × m × m × m × m

9m² = 3² × m × m

18nm² = 3² × 2 × n × m × m

Least common multiple of 36, 9, 18 is 3² ⋅ 2² 

= 36nm⁴

Problem 12 :

36m²n², 30n², 36n⁴

Solution:

36m²n² = 2² × 3² × m × m × n × n

30n² = 2 × 5 × 3 × n × n

36n⁴ =  2² × 3² × n × n × n × n

Least common multiple of 36, 30 is 3² ⋅ 2² ⋅ 5

= 180n⁴m²

Problem 13 :

16x²y, 32x

Solution:

16x²y = 2² × 2² × x × x × y

32x = 2² × 2² × 2 × x

Least common multiple of 16, 32 is 2² ⋅ 2² ⋅ 2

= 32x²y

Problem 14 :

30ab³, 20ab³

Solution:

30ab³ = 2 × 3 × 5 × a × b × b × b

20ab³ = 2² × 5 × a × b × b × b 

Least common multiple of 30, 20 is 2² ⋅ 5 ⋅ 3

= 60ab³

Problem 15 :

10ba, 20ba, 28ba

Solution:

10ba = 2 × 5 × b × a

20ba = 2² × 5 × b × a

28ba =  2² × 7 × b × a

Least common multiple of 10, 20, 28 is 2² ⋅ 5 ⋅ 7

= 140ba

Problem 16 :

8y², 16xy, 16y

Solution:

8y² = 2² × 2 × y × y

16xy = 2² × 2² × x × y

16y = 2² × 2² × x

Least common multiple of 8, 16, 16 is 2² ⋅ 2²

= 16y²x

Problem 17 :

28b², 20ab³, 16b⁴

Solution:

28b² = 2² × 7 × b × b

20ab³ = 2² × 5 × a × b × b × b

16b⁴ = 2² × 2² × b × b × b × b

Least common multiple of 28, 20, 16 is 2² ⋅ 2² ⋅ 7 ⋅ 5

= 560b⁴a

Problem 18 :

12xy², 39y³

Solution:

12xy² = 2² × 3 × x × y × y

39y³ = 3 × 13 × y × y × y

Least common multiple of 12, 39 is 2² ⋅ 3 ⋅ 13

= 156xy³

Problem 19 :

33u, 9v²u

Solution:

33u = 3 × 11 × u

9v²u = 3² × v × v × u

Least common multiple of 33, 9 is 3² ⋅ 11 

= 99v²u

Problem 20 :

30yx, 24y²x

Solution:

30yx = 2 × 3 × 5 × y × x

24y²x = 2² × 2 × 3 × y × y × x

Least common multiple of 30, 24 is 2² ⋅ 2 ⋅ 3 ⋅ 5

= 120y²x

Problem 21 :

30v, 40u²v

Solution:

30v = 2 × 3 × 5 × v

40u²v = 2² × 2 × 5 × u × u × v

Least common multiple of 30, 40 is 2² ⋅ 2 ⋅ 3 ⋅ 5

= 120u²v