Question

1. find the prime factors. fill in the table. find the lcm and gcf for the pair of numbers. hint: list all factors least to greatest. given: 16, 18 prime factors: 16=□·□·□·□ 18=□·□·□ 16 □ 2 2 2 18 □ □ 3 lcm □ □ 2 2 □ 3 lcm = □ 16 □ □ 2 2 18 □ 3 gcf □ gcf=

Explanation:

Step1: Prime factorize 16

$16 = 2 \cdot 2 \cdot 2 \cdot 2$

Step2: Prime factorize 18

$18 = 2 \cdot 3 \cdot 3$

Step3: Fill LCM table columns

Columns are prime factors: 2, 2, 2, 3, 3
16 row: $2, 2, 2, 2, \text{(blank)}$
18 row: $2, \text{(blank)}, \text{(blank)}, 3, 3$
LCM row: take max per column: $2, 2, 2, 3, 3$

Step4: Calculate LCM

$LCM = 2 \times 2 \times 2 \times 3 \times 3 = 72$

Step5: Fill GCF table columns

Columns are prime factors: 2, 2, 2, 3
16 row: $2, 2, 2, \text{(blank)}$
18 row: $2, \text{(blank)}, \text{(blank)}, 3$
GCF row: take min per column: $2, \text{(blank)}, \text{(blank)}, \text{(blank)}$

Step6: Calculate GCF

$GCF = 2$

Answer:

Prime factors:
$16=2 \cdot 2 \cdot 2 \cdot 2$
$18=2 \cdot 3 \cdot 3$

LCM Table:

16	2	2	2	2
LCM	2	2	2	3	3

$LCM=72$

GCF Table:

16	2	2	2
GCF	2

$GCF=2$