Part a: find the lcm of 7 and 12. show your work. (3 points)
part b: find the gcf of 56 and 96. show your work. (3 points)
part c: using the gcf you found in part b, rewrite 56 + 96 as two factors. one factor is the gcf and the other is the sum of two numbers that do not have a common factor. show your work.

A. 84; B. 8; C. 8 × 19

Step-by-step explanation:

Part A. Least common multiple

Step 1. List the prime factors of each.

7 = 7

12 = 2 × 2 × 3

Step 2: Multiply each factor the greatest number of times it occurs in either number.

7 has one 7; 12 has two 2s and one 3.

LCM = 7 × 2 × 2 × 3

LCM = 7 × 12

LCM = 84

Part B. Highest common factor

Find all the factors of 56 and 96.

Factors of 56: 1, 2, 4,     7, 8,      14,          28

Factors of 96: 1, 2, 4, 6,     8, 12,    16, 24,     32, 48

The highest factor that in both 56 and 96 is 8.

Part C. Factoring

56 + 96 = 8(7 + 12) = 8 × 19

The GCF is 8.

19 = 7 + 12 is the sum of two numbers that do not have a common factor.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction