60w=w+24w

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

w,1,w

Since w,1,w 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 w1,w1.

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 w1 is w itself.

w1=w

w occurs 1 time.

The LCM of w1,w1 is the result of multiplying all prime factors the greatest number of times they occur in either term.

w

w

Multiply each term in 60w=w+24w by w in order to remove all the denominators from the equation.

60w⋅w=w⋅w+24w⋅w

Cancel the common factor of w.

Cancel the common factor.

60w⋅w=w⋅w+24w⋅w

Rewrite the expression.

60=w⋅w+24w⋅w

60=w⋅w+24w⋅w

Simplify each term.

Multiply w by w.

60=w2+24w⋅w

Cancel the common factor of w.

Cancel the common factor.

60=w2+24w⋅w

Rewrite the expression.

60=w2+24

60=w2+24

60=w2+24

60=w2+24

Rewrite the equation as w2+24=60.

w2+24=60

Move all terms not containing w to the right side of the equation.

Subtract 24 from both sides of the equation.

w2=60-24

Subtract 24 from 60.

w2=36

w2=36

Take the square root of both sides of the equation to eliminate the exponent on the left side.

w=±36

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite 36 as 62.

w=±62

Pull terms out from under the radical, assuming positive real numbers.

w=±6

w=±6

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the ± to find the first solution.

w=6

Next, use the negative value of the ± to find the second solution.

w=-6

The complete solution is the result of both the positive and negative portions of the solution.

w=6,-6

w=6,-6

w=6,-6

w=6,-6

Solve for w 60/w=w+24/w