I can't understand this question very well. It's supposed to be about GCFs and LCMs.

Question

The question is: A restaurant receives a shipment of onions every 14 days, a shipment of salad greens every 6 days, and a shipment of potatoes every 8 days. The restaurant received shipments of all three items today. Use the dropdown menus to correctly complete both statements.

Answer 1

6, 8 and 14 have a LCM of 168

factor each into integer factors

6=3x2

8=2^3

14=7x2

take the product of each integer factor, with the highest exponent appearing

3x2, 2^3, 2x7 have LCM =3(2^3)(7) = 168

if they all arrived today, they'll next arrive all on the same day in 168 days from today

green deliveries

day: 6,12,18,24,30,36,42,48,54,60,66, 72,78,84,90,96,102,108,114,120,126,132,138,144, 150,156,162, 168, ...

potatoes deliveries

day: 8,16,24,32,40,48,56,64,72,80,88,96,104,112,120,128,136,144,162,168, ...

greens and potatoes show up together every 24th day: 0,24,48,72,144,168, ...

onion deliveries

day: 14,28,42,56, 70,84,98,112,126,140,154,168,...

onions and greens show up at the same day every 42nd day: days 0,42,84,126, 168, ...

onions and potatoes show up at the same day every 56th day. days 0,56, 112, 168, ...

all 3 show up only every 168th day: days 0, 168, 336,...

24,42,56 have LCM=168

=2^3(3), 7(3)(2^2), 7(2^3) have LCM = 2^3(3)(7) = 168