Question

Find the H.C.F and L.C.M of
6x^2y and 4xy^2

Answer 1

Answer:

step by step is a correct answer

Answer 2

Answer:

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Algebra Examples

Popular Problems Algebra Find the LCM 4xy^2 , 6x^2y^3

4

x

y

2

,

6

x

2

y

3

Since

4

x

y

2

,

6

x

2

y

3

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

4

,

6

then find LCM for the variable part

x

1

,

y

2

,

x

2

,

y

3

.

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.

4

has factors of

2

and

2

.

2

⋅

2

6

has factors of

2

and

3

.

2

⋅

3

The LCM of

4

,

6

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

2

⋅

2

⋅

3

The LCM of

4

,

6

is

2

⋅

2

⋅

3

=

12

.

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12

The factor for

x

1

is

x

itself.

x

1

=

x

x

occurs

1

time.

The factors for

y

2

are

y

⋅

y

, which is

y

multiplied by each other

2

times.

y

2

=

y

⋅

y

y

occurs

2

times.

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 factors for

y

3

are

y

⋅

y

⋅

y

, which is

y

multiplied by each other

3

times.

y

3

=

y

⋅

y

⋅

y

y

occurs

3

times.

The LCM of

x

1

,

y

2

,

x

2

,

y

3

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

x

⋅

y

⋅

y

Multiply

y

by

y

by adding the exponents.

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x

y

2

The LCM for

4

x

y

2

,

6

x

2

y

3

is the numeric part

12

multiplied by the variable part.

12

x

y

2