Learning Task 4: Apply the LCM and GCF in solving the word problems below. Write your answer in your notebook.

1. Mary has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How wide should she cut the strips?

2. Jerwin exercises every 12 days and Nikki every 8 days. Jerwin and Nikki both exercised today. How many days will be until they exercise together again?

3. Cean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?

Paki answer po!

Least Common Multiple is also referred to as the Lowest Common Multiple and Least Common Divisor. For two integers a and b, the LCM is the smallest positive integer that is evenly divisible by a and b. For example, LCM(2,3) = 6. Derived using prime factorization. Aside from prime factorization, continuous division is also used.

Answers:

9 inches wide
24th day
2 pieces

Solutions:

1. Given: 72 inches wide piece of cloth

90 inches wide piece of cloth

Asked: The width of the strips that Mary should cut.

Answer:

Find the factors of 72 and 90.

72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 36, 72

90 - 1, 2, 3, 5, 6, 9, 10, 15, 30, 45, 90

List all the common factors.

72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 36, 72

90 - 1, 2, 3, 5, 6, 9, 10, 15, 30, 45, 90

Common Factors: 1, 2, 3, 6, 9

Choose the greatest.

GCF = 9

Therefore, the strips should be 9 inches wide.

2. Given: every 12 days - Jerwin's exercise schedule

every 8 days - Nikki's exercise schedule

Asked: The number of days until Jerwin and Nikki will exercise together again.

Answer:

Find the multiples.

12 - 12, 24, 36, 48, 60, 72, 84. 96, 108. 120

8 - 8, 16, 24, 32, 40, 48, 64, 72, 80

List all the common multiples.

12 - 12, 24, 36, 48, 60, 72, 84. 96, 108. 120

8 - 8, 16, 24, 32, 40, 48, 64, 72, 80______

Common Multiples: 24, 48, 72

Choose the lowest.

LCM = 24

Therefore, both Jerwin and Nikki will have their exercises together on the 24th day.

3. Given: 8 - inch pieces of toy train truck

18 - inch pieces of train truck

Asked: The number of pieces each child need to build truck which are equal in length.

Answer:

Find the factors of 8 and 18.

8 - 1, 2, 4, 8

18 - 1, 2, 3, 6, 9, 18

List all the common factors.

8 - 1, 2, 4, 8

18 - 1, 2, 3, 6, 9, 18

Common Factors: 1, 2

Choose the greatest.

GCF = 2

Therefore, each child need 2 pieces of toy train truck.

What is least common multiple: https://brainly.ph/question/18362060

What is greatest common factor: https://brainly.ph/question/2738874

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