Solved on Mar 17, 2024

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

STEP 1

1. LCM stands for Least Common Multiple, which is the smallest number that is a multiple of both numbers.
2. GCF stands for Greatest Common Factor, which is the largest number that divides both numbers without a remainder.
3. The list method involves listing the multiples or factors of the given numbers and finding the least common or greatest common one.

STEP 2

1. Find the LCM of 14 and 8 by listing multiples.
2. Find the GCF of 12 and 18 by listing factors.
3. Find the LCM of 70 and 40 by listing multiples.
4. Find the GCF of 70 and 182 by listing factors.

STEP 3

List the multiples of 14 and 8.
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, ...

STEP 4

Identify the least common multiple of 14 and 8 from the lists.
The LCM of 14 and 8 is 56.

STEP 5

List the factors of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18

STEP 6

Identify the greatest common factor of 12 and 18 from the lists.
The GCF of 12 and 18 is 6.

STEP 7

List the multiples of 70 and 40.
Multiples of 70: 70, 140, 210, 280, 350, 420, ... Multiples of 40: 40, 80, 120, 160, 200, 240, 280, ...

STEP 8

Identify the least common multiple of 70 and 40 from the lists.
The LCM of 70 and 40 is 280.

STEP 9

List the factors of 70 and 182.
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182

STEP 10

Identify the greatest common factor of 70 and 182 from the lists.
The GCF of 70 and 182 is 14.
The solutions are: (a) $\operatorname{LCM}(14,8) = 56$ (b) $\operatorname{GCF}(12,18) = 6$ (c) $\operatorname{LCM}(70,40) = 280$ (d) $\operatorname{GCF}(70,182) = 14$

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Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

STEP 1

STEP 2

1. Find the LCM of 14 and 8 by listing multiples.
2. Find the GCF of 12 and 18 by listing factors.
3. Find the LCM of 70 and 40 by listing multiples.
4. Find the GCF of 70 and 182 by listing factors.

STEP 3

List the multiples of 14 and 8.
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, ...

STEP 4

Identify the least common multiple of 14 and 8 from the lists.
The LCM of 14 and 8 is 56.

STEP 5

List the factors of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18

STEP 6

Identify the greatest common factor of 12 and 18 from the lists.
The GCF of 12 and 18 is 6.

STEP 7

List the multiples of 70 and 40.
Multiples of 70: 70, 140, 210, 280, 350, 420, ... Multiples of 40: 40, 80, 120, 160, 200, 240, 280, ...

STEP 8

Identify the least common multiple of 70 and 40 from the lists.
The LCM of 70 and 40 is 280.

STEP 9

List the factors of 70 and 182.
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182

STEP 10

Identify the greatest common factor of 70 and 182 from the lists.
The GCF of 70 and 182 is 14.
The solutions are: (a) $\operatorname{LCM}(14,8) = 56$ (b) $\operatorname{GCF}(12,18) = 6$ (c) $\operatorname{LCM}(70,40) = 280$ (d) $\operatorname{GCF}(70,182) = 14$

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Find the LCM⁡\operatorname{LCM}LCM and GCF⁡\operatorname{GCF}GCF of given numbers using the list method. Additional materials: eBook.

STEP 1

STEP 2

1. Find the LCM of 14 and 8 by listing multiples.2. Find the GCF of 12 and 18 by listing factors.3. Find the LCM of 70 and 40 by listing multiples.4. Find the GCF of 70 and 182 by listing factors.

STEP 3

List the multiples of 14 and 8.Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, ...

STEP 4

Identify the least common multiple of 14 and 8 from the lists.The LCM of 14 and 8 is 56.

STEP 5

List the factors of 12 and 18.Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18

STEP 6

Identify the greatest common factor of 12 and 18 from the lists.The GCF of 12 and 18 is 6.

STEP 7

List the multiples of 70 and 40.Multiples of 70: 70, 140, 210, 280, 350, 420, ... Multiples of 40: 40, 80, 120, 160, 200, 240, 280, ...

STEP 8

Identify the least common multiple of 70 and 40 from the lists.The LCM of 70 and 40 is 280.

STEP 9

List the factors of 70 and 182.Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182

STEP 10

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the $\operatorname{LCM}$ and $\operatorname{GCF}$ of given numbers using the list method. Additional materials: eBook.

1. Find the LCM of 14 and 8 by listing multiples.
2. Find the GCF of 12 and 18 by listing factors.
3. Find the LCM of 70 and 40 by listing multiples.
4. Find the GCF of 70 and 182 by listing factors.

List the multiples of 14 and 8.
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ... Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, ...

Identify the least common multiple of 14 and 8 from the lists.
The LCM of 14 and 8 is 56.

List the factors of 12 and 18.
Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18

Identify the greatest common factor of 12 and 18 from the lists.
The GCF of 12 and 18 is 6.

List the multiples of 70 and 40.
Multiples of 70: 70, 140, 210, 280, 350, 420, ... Multiples of 40: 40, 80, 120, 160, 200, 240, 280, ...

Identify the least common multiple of 70 and 40 from the lists.
The LCM of 70 and 40 is 280.

List the factors of 70 and 182.
Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70 Factors of 182: 1, 2, 7, 13, 14, 26, 91, 182