(n-2)⋅180n=150

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

1,n,1

Since 1,n,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1 then find LCM for the variable part n1.

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 number 1 is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of 1,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

1

The factor for n1 is n itself.

n1=n

n occurs 1 time.

The LCM of n1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

n

n

Multiply each term in (n-2)⋅180n=150 by n in order to remove all the denominators from the equation.

(n-2)⋅180n⋅n=150⋅n

Simplify (n-2)⋅180n⋅n.

Multiply n-2 and 180n.

(n-2)⋅180n⋅n=150⋅n

Cancel the common factor of n.

Cancel the common factor.

(n-2)⋅180n⋅n=150⋅n

Rewrite the expression.

(n-2)⋅180=150⋅n

(n-2)⋅180=150⋅n

Apply the distributive property.

n⋅180-2⋅180=150⋅n

Simplify the expression.

Move 180 to the left of n.

180⋅n-2⋅180=150⋅n

Multiply -2 by 180.

180n-360=150⋅n

180n-360=150⋅n

180n-360=150n

180n-360=150n

Move all terms containing n to the left side of the equation.

Subtract 150n from both sides of the equation.

180n-360-150n=0

Subtract 150n from 180n.

30n-360=0

30n-360=0

Add 360 to both sides of the equation.

30n=360

Divide each term by 30 and simplify.

Divide each term in 30n=360 by 30.

30n30=36030

Cancel the common factor of 30.

Cancel the common factor.

30n30=36030

Divide n by 1.

n=36030

n=36030

Divide 360 by 30.

n=12

n=12

n=12

Solve for n (n-2)*180/n=150