Question

Find the LCM of 15x2y,12xy,3y2​

Answer 1

xy is the LCM
as all the terms have one variable and in total there are two variables so the lcm will be xy

Answer 2

Answer:

Mark as brainliest mate !

Step-by-step explanation:

Since  

12

x

y

,

20

x

2

contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part  

12

,

20

then find LCM for the variable part  

x

1

,

y

1

,

x

2

.

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The prime factors for  

12

are  

2

⋅

2

⋅

3

.

Tap for more steps...

2

⋅

2

⋅

3

The prime factors for  

20

are  

2

⋅

2

⋅

5

.

Tap for more steps...

2

⋅

2

⋅

5

The LCM of  

12

,

20

is the result of multiplying all prime factors the greatest number of times they occur in either number.

2

⋅

2

⋅

3

⋅

5

The LCM of  

12

,

20

is  

2

⋅

2

⋅

3

⋅

5

=

60

.

Tap for more steps...

60

The factor for  

x

1

is  

x

itself.

x

1

=

x

x

occurs  

1

time.

The factor for  

y

1

is  

y

itself.

y

1

=

y

y

occurs  

1

time.

The factors for  

x

2

are  

x

⋅

x

, which is  

x

multiplied by each other  

2

times.

x

2

=

x

⋅

x

x

occurs  

2

times.

The LCM of  

x

1

,

y

1

,

x

2

is the result of multiplying all prime factors the greatest number of times they occur in either term.

x

⋅

y

Multiply  

x

by  

y

.

x

y

The LCM for  

12

x

y

,

20

x

2

is the numeric part  

60

multiplied by the variable part.

60

x

y

Since  

12

x

y

,

20

x

2

contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part  

12

,

20

then find LCM for the variable part  

x

1

,

y

1

,

x

2

.

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The prime factors for  

12

are  

2

⋅

2

⋅

3

.

Tap for more steps...

2

⋅

2

⋅

3

The prime factors for  

20

are  

2

⋅

2

⋅

5

.

Tap for more steps...

2

⋅

2

⋅

5

The LCM of  

12

,

20

is the result of multiplying all prime factors the greatest number of times they occur in either number.

2

⋅

2

⋅

3

⋅

5

The LCM of  

12

,

20

is  

2

⋅

2

⋅

3

⋅

5

=

60

.

Tap for more steps...

60

The factor for  

x

1

is  

x

itself.

x

1

=

x

x

occurs  

1

time.

The factor for  

y

1

is  

y

itself.

y

1

=

y

y

occurs  

1

time.

The factors for  

x

2

are  

x

⋅

x

, which is  

x

multiplied by each other  

2

times.

x

2

=

x

⋅

x

x

occurs  

2

times.

The LCM of  

x

1

,

y

1

,

x

2

is the result of multiplying all prime factors the greatest number of times they occur in either term.

x

⋅

y

Multiply  

x

by  

y

.

x

y

The LCM for  

12

x

y

,

20

x

2

is the numeric part  

60

multiplied by the variable part.

60

x

y