Match each set of numbers with their least common multiple. 288 44 504 84 200 108

27, 12, and 36→

25 and 8→

14 and 12→

9, 8, and 7→

22 and 4→

32, 24, and 18→

Least Common Multiple Calculator

Brute Force Method

There are multiple ways to find a least common multiple. The most basic is simply using a "brute force" method that lists out each integer's multiples.

EX: Find LCM(18, 26)

18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, 198, 216, 234

26: 52, 78, 104, 130, 156, 182, 208, 234

As can be seen, this method can be fairly tedious, and is far from ideal.

Prime Factorization Method

A more systematic way to find the LCM of some given integers is to use prime factorization. Prime factorization involves breaking down each of the numbers being compared into its product of prime numbers. The LCM is then determined by multiplying the highest power of each prime number together. Note that computing the LCM this way, while more efficient than using the "brute force" method, is still limited to smaller numbers. Refer to the example below for clarification on how to use prime factorization to determine the LCM:

EX: Find LCM(21, 14, 38)

21 = 3 × 7

14 = 2 × 7

38 = 2 × 19

The LCM is therefore:

3 × 7 × 2 × 19 = 798

Greatest Common Divisor Method

A third viable method for finding the LCM of some given integers is using the greatest common divisor. This is also frequently referred to as the greatest common factor (GCF), among other names. Refer to the link for details on how to determine the greatest common divisor. Given LCM(a, b), the procedure for finding the LCM using GCF is to divide the product of the numbers a and b by their GCF, i.e. (a × b)/GCF(a,b). When trying to determine the LCM of more than two numbers, for example LCM(a, b, c) find the LCM of a and b where the result will be q. Then find the LCM of c and q. The result will be the LCM of all three numbers. Using the previous example:

EX: Find LCM(21, 14, 38)

GCF(14, 38) = 2

LCM(14, 38) =

38 × 14

2

= 266

GCF(266, 21) = 7

LCM(266, 21) =

266 × 21

7

= 798

LCM(21, 14, 38) = 798

Note that it is not important which LCM is calculated first as long as all the numbers are used, and the method is followed accurately. Depending on the particular situation, each method has its own merits, and the user can decide which method to pursue at their own discretion.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is