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RV-12-001 · Repeating schedules and simultaneous events

Two warning lights flash together at 09:00. Light A then flashes every 19 minutes and light B every 12 minutes. They run for 540 minutes.

(a) Find the time when the two lights next flash together.

(b) How many times do they flash together after 09:00, up to and including the end of the run?

Part (a) LCM in Context (Simultaneous Flashing Lights) Booklet p. 42 & p. 54
Method
1) Find LCM of the two intervals using prime factors / Venn diagram
2) Convert LCM minutes to hours & minutes and add to 09:00
3) Divide total run time by LCM
Worked Example (RV-12-001 · Part (a))
Find the time when the two lights next flash together.
1)
Prime factorise each number: 19=1919=19, 12=2×2×312=2\times2\times3.
2)
191219none2 · 2 · 3
3)
Place each shared prime in the intersection once. Multiply all factors in the diagram: LCM = 228.
4)
The next shared flash is 228 minutes after 09:00: 12:48.
Ans = 12:48
Part (b) LCM in Context (Simultaneous Flashing Lights) Booklet p. 42 & p. 54
Method
1) Find LCM of the two intervals using prime factors / Venn diagram
2) Convert LCM minutes to hours & minutes and add to 09:00
3) Divide total run time by LCM
Worked Example (RV-12-001 · Part (b))
How many times do they flash together after 09:00, up to and including the end of the run?
1)
Prime factorise each number: 19=1919=19, 12=2×2×312=2\times2\times3.
2)
191219none2 · 2 · 3
3)
Place each shared prime in the intersection once. Multiply all factors in the diagram: LCM = 228.
4)
After the starting flash, shared flashes occur every 228 minutes. ⌊540228⌋=2\left\lfloor\frac{540}{228}\right\rfloor=2 flashes fall within the run.
Ans = 2