Question

hint: list all factors least to greatest. given: 42, 68 prime factors: 42 = 2 · 3 · 7 68 = 2 · 2 · 17 42: 2, 3, 7 68: 2, 2, 17 lcm: blank, blank, blank, blank, blank lcm = 1428 42: blank, blank, blank 68: blank, blank, blank gcf: blank gcf = 2

Explanation:

Step1: Fill LCM prime factors

To find LCM, take the highest power of each prime factor present in 42 and 68. The primes are 2 (highest power $2^2$), 3 ($3^1$), 7 ($7^1$), 17 ($17^1$). So the LCM row is: 2, 2, 3, 7, 17

Step2: Fill GCF prime factors

To find GCF, take the lowest power of common prime factors. The only common prime is 2 (lowest power $2^1$). First, fill the prime factors for 42 and 68 rows:

• 42 row: 2, 3, 7
• 68 row: 2, 2, 17

Then the GCF row is: 2

Answer:

LCM row (left to right): 2, 2, 3, 7, 17

42 row (GCF section, left to right): 2, 3, 7

68 row (GCF section, left to right): 2, 2, 17

GCF row: 2

Final LCM: 1428, Final GCF: 2