Finite Math Examples

y + 0

$y + 0$ ,

942 y - 37

$942 y - 37$ ,

68

$68$

Step 1

Since

y, 942 y - 37, 68

$y, 942 y - 37, 68$ contains both numbers and variables, there are four steps to find the LCM. Find LCM for the numeric, variable, and compound variable parts. Then, multiply them all together.

Steps to find the LCM for

y, 942 y - 37, 68

$y, 942 y - 37, 68$ are:

1. Find the LCM for the numeric part

1, 1, 68

$1, 1, 68$ .

2. Find the LCM for the variable part

y^{1}

$y^{1}$ .

3. Find the LCM for the compound variable part

942 y - 37

$942 y - 37$ .

4. Multiply each LCM together.

Step 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.

Step 3

The number

1

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

Not prime

Step 4

The prime factors for

68

$68$ are

2 \cdot 2 \cdot 17

$2 \cdot 2 \cdot 17$ .

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Step 4.1

68

$68$ has factors of

2

$2$ and

34

$34$ .

2 \cdot 34

$2 \cdot 34$

Step 4.2

34

$34$ has factors of

2

$2$ and

17

$17$ .

2 \cdot 2 \cdot 17

$2 \cdot 2 \cdot 17$

2 \cdot 2 \cdot 17

$2 \cdot 2 \cdot 17$

Step 5

Multiply

2 \cdot 2 \cdot 17

$2 \cdot 2 \cdot 17$ .

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

4 \cdot 17

$4 \cdot 17$

Step 5.2

Multiply

4

$4$ by

17

$17$ .

68

$68$

68

$68$

Step 6

The factor for

y^{1}

$y^{1}$ is

y

$y$ itself.

y^{1} = y

$y^{1} = y$

y

$y$ occurs

1

$1$ time.

Step 7

The LCM of

y^{1}

$y^{1}$ is the result of multiplying all prime factors the greatest number of times they occur in either term.

y

$y$

Step 8

The factor for

942 y - 37

$942 y - 37$ is

942 y - 37

$942 y - 37$ itself.

(942 y - 37) = 942 y - 37

$(942 y - 37) = 942 y - 37$

(942 y - 37)

$(942 y - 37)$ occurs

1

$1$ time.

Step 9

The LCM of

942 y - 37

$942 y - 37$ is the result of multiplying all factors the greatest number of times they occur in either term.

942 y - 37

$942 y - 37$

Step 10

The Least Common Multiple

LCM

$LCM$ of some numbers is the smallest number that the numbers are factors of.

68 y (942 y - 37)

$68 y (942 y - 37)$