-7 , 1.1 , 12 , -110 , -1.3

To find the LCM for a list of fractions, check if denominators are similar or not.

Fractions with the same denominator:

1: LCM(ab,cb)=LCM(a,c)b

Fractions with different denominators such as, LCM(ab,cd):

1: Find the LCM of b and d=LCM(b,d)

2: Multiply the numerator and denominator of the first fraction ab by LCM(b,d)b

3: Multiply the numerator and denominator of the second fraction cd by LCM(b,d)d

4: After making the denominators for all the fractions same, in this case, only two fractions, find the LCM of the new numerators

5: The LCM will be the LCM(numerators)LCM(b,d)

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

Since 2 has no factors besides 1 and 2.

2 is a prime number

10 has factors of 2 and 5.

2⋅5

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

Not prime

The LCM of 1,1,2,10,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅5

Multiply 2 by 5.

10

10

Multiply the numerator and denominator of -71 by 10.

-7⋅101⋅10

Multiply -7 by 10.

-701⋅10

Multiply 10 by 1.

-7010

Divide 10 by 1.

10

Multiply the numerator and denominator of 1.11 by 10.

1.1⋅101⋅10

Multiply 1.1 by 10.

111⋅10

Multiply 10 by 1.

1110

Divide 10 by 2.

5

Multiply the numerator and denominator of 12 by 5.

1⋅52⋅5

Multiply 5 by 1.

52⋅5

Multiply 2 by 5.

510

Divide 10 by 10.

1

Multiply the numerator and denominator of -110 by 1.

-1⋅110⋅1

Multiply -1 by 1.

-110⋅1

Multiply 10 by 1.

-110

Divide 10 by 1.

10

Multiply the numerator and denominator of -1.31 by 10.

-1.3⋅101⋅10

Multiply -1.3 by 10.

-131⋅10

Multiply 10 by 1.

-1310

The new list with the same denominator is -7010,1110,510,-110,-1310.

-7010,1110,510,-110,-1310

-7010,1110,510,-110,-1310

Multiply each number by 10 to get rid of decimals.

700,110,50,10,130

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.

Since the LCM is the smallest positive number, LCM(700,110,50,10,130)=LCM(700,110,50,10,130)

The prime factors for 700 are 2⋅2⋅5⋅5⋅7.

700 has factors of 2 and 350.

2⋅350

350 has factors of 2 and 175.

2⋅2⋅175

175 has factors of 5 and 35.

2⋅2⋅5⋅35

35 has factors of 5 and 7.

2⋅2⋅5⋅5⋅7

2⋅2⋅5⋅5⋅7

The prime factors for 110 are 2⋅5⋅11.

110 has factors of 2 and 55.

2⋅55

55 has factors of 5 and 11.

2⋅5⋅11

2⋅5⋅11

The prime factors for 50 are 2⋅5⋅5.

50 has factors of 2 and 25.

2⋅25

25 has factors of 5 and 5.

2⋅5⋅5

2⋅5⋅5

10 has factors of 2 and 5.

2⋅5

The prime factors for 130 are 2⋅5⋅13.

130 has factors of 2 and 65.

2⋅65

65 has factors of 5 and 13.

2⋅5⋅13

2⋅5⋅13

The LCM of 700,110,50,10,130 is the result of multiplying all prime factors the greatest number of times they occur in either number.

2⋅2⋅5⋅5⋅7⋅11⋅13

The LCM of 700,110,50,10,130 is 2⋅2⋅5⋅5⋅7⋅11⋅13=100100.

Multiply 2 by 2.

4⋅5⋅5⋅7⋅11⋅13

Multiply 4 by 5.

20⋅5⋅7⋅11⋅13

Multiply 20 by 5.

100⋅7⋅11⋅13

Multiply 100 by 7.

700⋅11⋅13

Multiply 700 by 11.

7700⋅13

Multiply 7700 by 13.

100100

100100

Since we multiplied by 10 to get rid of the decimals, divide the answer by 10.

10010

10010

Divide the LCM of -70,11,5,-1,-13 by the LCM of 1,1,2,10,1.

1001010

Divide 10010 by 10.

1001

1001

Find the LCM -7 , 1.1 , 1/2 , -1/10 , -1.3