Basic Functions
Advanced

LCM of three cycles: when do they all line up?

LCM takes more than two numbers.

Task:

Three buses leave the depot together at 07:00 and repeat every few minutes. In E2:E4 give how many minutes pass before all three routes on each line leave together again.

Interactive Spreadsheet

Read about GCD, LCM

Hints

+5 XPno-hints bonus

Solve it on your own to keep the bonus. Each hint gets one step closer to the formula.

Variations of GCD, LCM

0/3

The same formula in the other shapes it takes at work.

  1. GCD and LCM Functions

    Two maintenance cycles, and the arithmetic for putting them on one calendar.

    Core
    Advanced
  2. Simplify a ratio with GCD

    Divide both sides by their greatest common divisor.

    Advanced
  3. LCM of three cycles: when do they all line up?

    LCM takes more than two numbers.

    Advanced

The data in this exercise

This is the grid you start with. Cell references in the task — B6, C2 — point at the row numbers and column letters below.

4 rows × 5 columns3 cells you fill in
ABCDE
1LineRoute 1 (min)Route 2 (min)Route 3 (min)Together again
2North121520
3South81025
4East6914
What this exercise teachesMay contain the answer

LCM extends to any number of values, which is what makes it useful for timetables, maintenance cycles and stock counts that each run on their own rhythm. The East line only lines up every 126 minutes — worth knowing before promising a connection.