Number and Operations Session 6: Solutions

A B
Homework

Solutions for Session6, Part A

See solutions for Problems: A1 | A2 | A3 | A4 | A5 | A6

Problem A1

18 = 2 • 3 • 3, and 30 = 2 • 3 • 5. The factors they have in common are 2 and 3. In the left circle is 3, and in the right circle is 5:

The GCF is the product of all the numbers in the intersection: 2 • 3 = 6. The GCF is 6.

The LCM is the product of all the numbers in the Venn diagram: 3 • 2 • 3 • 5 = 90. The LCM is 90.

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Problem A2

d.	All three methods yield the same prime numbers (two factors of 2, one factor of 3, and one factor of 5).

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Problem A3

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Problem A4

The intersection contains the only common factor, which is 3. On the left are the factors of 231 that are not factors of 195; i.e., 7 and 11. On the right are the factors of 195 that are not factors of 231; i.e., 5 and 13.

The GCF is the product of all the numbers in the intersection (in this case, just the 3). The GCF is 3.

The LCM is the product of all the numbers in the Venn diagram: 7 • 11 • 3 • 5 • 13 = 15,015. The LCM is 15,015.

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Problem A5

The largest square that can tile this entire rectangle without any gaps or overlap is 6 by 6. Therefore, the GCF of 30 and 42 is 6.

The smallest square that could be tiled by this rectangle is 210 by 210. Therefore, the LCM of 30 and 42 is 210.

The largest square that can tile this entire rectangle without any gaps or overlap is 6 by 6. Therefore, the GCF of 18 and 30 is 6.

The smallest square that could be tiled by this rectangle is 90 by 90. Therefore, the LCM of 18 and 30 is 90.

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Problem A6

Answers will vary.

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Session6 | Notes | Solutions | Video