Phase 1 of 5

Mission XP

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Phase 1 — Mission Briefing

Space Mission Control

Welcome, Cadet. You have been selected to join NASA's deep-space exploration team. Your mission: plan, coordinate, and launch a fleet of spacecraft using the power of GCF, LCM, and factor analysis.

Mission Dossier

The year is 2087. Earth's Space Exploration Command (SEC) needs your mathematical expertise to coordinate a multi-craft mission to the outer solar system. Every launch window, orbit synchronization, and supply schedule depends on your ability to find Greatest Common Factors, Least Common Multiples, and work with prime factorization.

You will progress through 5 mission phases, each building on the last. Complete all tasks to earn your Mission Commander certification!

Cadet Name

Class Period

Date

Mission Objectives (Learning Goals)

★ Find GCF using prime factorization

★ Find LCM using prime factorization

★ Apply GCF & LCM to real-world problems

▸Identify factors and multiples of whole numbers
▸Use prime factorization to find the GCF and LCM of two or more numbers
▸Apply the distributive property using GCF
▸Solve real-world problems involving GCF and LCM
▸Create and interpret factor trees and Venn diagrams

Select Your Difficulty Level

Support Mode includes extra vocabulary help and step-by-step guides. Challenge Mode adds bonus tasks and higher numbers.

Phase 2 — Research & Discover

Deep Space Data Lab

Before launching any spacecraft, you must master the mathematics of space coordination. Analyze orbital data, decode transmissions, and build your factor analysis skills.

Interactive Factor Tree Reference

Study these factor trees carefully. Purple circles show prime numbers — the building blocks of all numbers.

2.1

Orbital Period Analysis

Three satellites orbit different planets. Their orbital periods are:

Satellite	Planet	Orbital Period (hours)
🌐 Alpha-7	Mars	24
🌑 Beta-3	Jupiter	36
⭐ Gamma-9	Saturn	18

List all factors of 24:

List all factors of 36:

List all factors of 18:

What is the GCF of 24, 36, and 18? Show your work:

GCF =

In your own words, what does the GCF tell us about these satellites?

The GCF is the largest number that divides evenly into ALL three periods. Try breaking each number into prime factors first: 24 = 2³ × 3, 36 = 2² × 3², 18 = 2 × 3². Then take the lowest power of each shared prime.

Vocabulary Support:

Factor: A number that divides into another number with no remainder.
GCF (Greatest Common Factor): The biggest factor shared by all numbers.
Prime number: A number with exactly 2 factors: 1 and itself (like 2, 3, 5, 7).

2.2

Supply Crate Scheduling

The space station receives deliveries on two schedules:

Food supplies: every 12 days
Fuel cells: every 8 days

Both were last delivered on Day 0. When will they next arrive on the same day?

Prime factorization of 12:

Prime factorization of 8:

LCM of 12 and 8:

Explain what the LCM means in this situation:

LCM = Least Common Multiple. To find it using prime factorization, take the HIGHEST power of each prime factor. 12 = 2² × 3, 8 = 2³. Highest powers: 2³ and 3¹ = 8 × 3 = ?

2.3

Crew Rotation Patterns

Three teams rotate duties on the station:

Team	Rotation Cycle
🔴 Navigation Team	Every 15 days
🔵 Engineering Team	Every 20 days
🟠 Science Team	Every 10 days

Find the LCM of 15, 20, and 10. Show all work:

LCM =

How many times will all three teams be on duty together in one year (365 days)?

Explain your reasoning:

⚡

Challenge: If a fourth team rotates every 14 days, find the new LCM of all four teams.

⚙ GCF / LCM Calculator

Use this tool to check your work. Enter two numbers to find their GCF and LCM.

Number A

Number B

Enter two numbers above and click Calculate

2.4

Distributive Property in Space

The supply officer needs to distribute 36 oxygen tanks and 48 water containers equally among cargo bays with no leftover items.

What is the greatest number of cargo bays possible?

How many oxygen tanks per bay?

How many water containers per bay?

Write the expression using the distributive property: 36 + 48 = GCF × (? + ?)

The distributive property says: a + b = GCF(a,b) × (a/GCF + b/GCF). Find GCF(36, 48) first, then divide each number by the GCF.

Phase 3 — Plan & Design

Mission Planning Center

Using your research, plan the launch schedule, crew assignments, and supply distribution for a 6-month deep-space expedition.

3.1

Launch Window Planning

You have 3 rockets that need to launch in synchronized windows. Their preparation cycles are:

Rocket	Prep Cycle (days)	Prime Factorization
🚀 Falcon-X	28
🚀 Nova-II	42
🚀 Titan-V	35

What is the LCM of 28, 42, and 35?

If all rockets launched on Day 0, when is the next day ALL three can launch together?

Create a Venn diagram showing the prime factors. You can sketch below or describe it:

3.2

Crew Assignment Optimization

You have 72 astronauts and 54 scientists to organize into mixed teams. Each team must have equal numbers of astronauts AND equal numbers of scientists.

What is the maximum number of teams you can create?

Astronauts per team:

Scientists per team:

Write the distributive property expression: 72 + 54 = GCF × (? + ?)

Give your teams creative space-themed names! List at least 3:

3.3

Communication Schedule Design

Design a communication schedule for three deep-space probes. Each probe sends a signal at regular intervals:

📡

Probe Artemis

Every 16 min

📡

Probe Apollo

Every 20 min

📡

Probe Mercury

Every 30 min

Find the LCM of 16, 20, and 30:

LCM =

If all probes transmitted at 8:00 AM, when do all three transmit again at the same time?

Fill in the table — mark an X when each probe transmits (up to 120 min):

Probe	16	20	30	32	40	48	60	64	80	90	96	100	112	120
Artemis (16)
Apollo (20)
Mercury (30)

3.4

Design Your Mission Patch

Every NASA mission has a patch. Design yours! Use the drawing canvas below. Your patch must include at least one mathematical symbol or number related to GCF/LCM.

Describe your mission patch design and the math it represents:

Phase 4 — Build & Create

Mission Execution

It is time to put your plans into action. Solve complex multi-step problems to successfully launch, navigate, and resupply your fleet.

4.1

Multi-Ship Fuel Management

Three ships carry different fuel amounts. You must divide fuel equally into transfer pods.

Ship	Fuel Units	Prime Factorization
Voyager-1	120
Voyager-2	84
Voyager-3	156

What is the largest pod size that works for ALL ships (GCF of 120, 84, 156)?

GCF =

How many pods does each ship fill?

Voyager-1

Voyager-2

Voyager-3

Write the distributive property for 120 + 84 + 156:

4.2

Navigation Grid Puzzle

You need to tile the navigation display with identical square tiles (no cutting). The display is 180 cm wide and 240 cm tall.

What is the side length of the largest possible square tile? (GCF of 180 and 240)

Largest tile side =

How many tiles across?

How many tiles down?

Total number of tiles needed?

4.3

Asteroid Belt Timing

Three asteroid clusters pass through your flight path at regular intervals:

Cluster Alpha: every 45 minutes
Cluster Beta: every 60 minutes
Cluster Gamma: every 72 minutes

All three clusters just passed at 0 minutes. You need to find safe windows between encounters.

Find the LCM of 45, 60, and 72:

LCM =

When is the next time ALL three clusters pass at the same moment?

How many safe windows exist in a 24-hour period (1440 minutes) when NONE of the clusters are passing? Explain your strategy:

⚡

Challenge: If you can only fly when EXACTLY ONE cluster is present, how many minutes in a 12-hour period allow travel?

4.4

Supply Manifest Challenge

Create a supply manifest for a deep-space station. You must package items in equal groups.

Supply Item	Quantity	Your Package Size (GCF)	Number of Packages
Freeze-dried meals	144
Water pouches	108
Oxygen canisters	90

GCF of 144, 108, and 90:

Write the expression: 144 + 108 + 90 = GCF × (? + ? + ?)

Now create your OWN supply problem using two numbers between 50 and 200. State the problem and solve it:

4.5

Mission Log Entry

Write a mission log entry (at least 4 sentences) describing one scenario where you used GCF or LCM during your mission. Include:

The real-world situation
The specific numbers involved
How you solved it (which method)
Why the answer made sense

Mission Log — Entry #1

Phase 5 — Present & Reflect

Mission Debrief

Your mission is complete, Commander. Review your work, assess your performance, and reflect on what you learned.

Achievement Badges

Badges earned based on completed tasks across all phases.

Space Explorer

Completed Phase 1

Data Analyst

Completed Phase 2

Mission Planner

Completed Phase 3

Mission Commander

Completed Phase 4

GCF/LCM Master

All phases complete

Self-Assessment Rubric

Rate your performance honestly in each area.

Skill	Beginning (1)	Developing (2)	Proficient (3)	Advanced (4)
Finding Factors	I need more help	I can find some factors	I can find all factors	I can teach others
Prime Factorization	I need more help	I can do simple ones	I can do any number	I use exponent form
Finding GCF	I need more help	I can find GCF of 2 numbers	I can find GCF of 3+ numbers	I apply GCF to word problems
Finding LCM	I need more help	I can find LCM of 2 numbers	I can find LCM of 3+ numbers	I apply LCM to word problems
Distributive Property	I need more help	I know the idea	I can apply it	I can explain it

Reflection Journal

What was the most interesting thing you learned in this project?

Which task was the most challenging? What made it hard?

How might GCF and LCM be useful in your everyday life? Give at least 2 examples.

If you could add one more phase to this mission, what would it be?

Mission Portfolio Summary

Click "Generate Portfolio" to create your mission summary.

🚀

Mission Commander Certificate

Cadet Name

Has demonstrated outstanding mathematical skills and earned the rank of Commander.

Total XP

Tasks Done

Completion

Need help? Explore these

Trusted sites for GCF, LCM & Factors. Each opens in a new tab.

Vocabulary

Factor: A number that divides evenly into another number with no remainder.
GCF: Greatest Common Factor — the largest factor two numbers share.
LCM: Least Common Multiple — the smallest multiple two numbers share.
Multiple: The result of multiplying a number by 1, 2, 3, and so on.
Prime: A number greater than 1 whose only factors are 1 and itself.

Learn more

Helpful hints

Stuck on a step? Try these tips for GCF, LCM & Factors.

Space Mission Control

Mission Dossier

Mission Objectives (Learning Goals)

Select Your Difficulty Level

Deep Space Data Lab

Interactive Factor Tree Reference

⚙ GCF / LCM Calculator

Mission Planning Center

Mission Execution

Mission Debrief

Achievement Badges

Space Explorer

Data Analyst

Mission Planner

Mission Commander

GCF/LCM Master

Self-Assessment Rubric

Reflection Journal

Mission Portfolio Summary

Mission Score