The red lights will blink at seconds 3,6,9,12, etc.(all factors of 3 up to 60)
The blue lights will blink at seconds 5, 10, 15, etc.(all factors of 5 up to 60)
Considering this, they will blink simultaniously at intervals only common to factors of 5 and 3 ie. 15, 30, 45, and 60 only.
Answer: 4 times in 1 minute
Hope this helps:)