I have a maths problem and wanted to know if there was an easier way or a formula to work it out, rather than go through each time which is taking ages.

Problem - "Two cuckoo clocks were brought to the Tick Tock Clock Shop for repairs. Both clocks always told the correct time. However, one cuckoo came out every 45 minutes and the other came out every 55 minutes. One day, both cuckoos came out at 12.00 noon. When was the next time both cuckoos came out together."

If someone knows a way of working it out, that would be great. Thanks.