To find the topicId of a specific topic, follow these steps:

Send a retrieve topic list API request with the includeOnly parameter set to id and name (/services/v2/topic.json?includeOnly=id,name) to the TeamHub REST API.

Result: The system returns a list of all the topics on your site, along with information about those topics.

{"name":"","sort":"popularity","page":1,"pageSize":20,"pageCount":6,"listCount":20,"totalCount":112,"list":
[{"id":532,"name":"sun","usedCount":0},{"id":892,"name":"people","usedCount":0},
 {"id":541,"name":"animals","usedCount":0},
 {"id":531,"name":"dragons","usedCount":0},
 {"id":555,"name":"flowers","usedCount":0},
 {"id":542,"name":"work","usedCount":0},
 {"id":538,"name":"food fun","usedCount":0},                                   
 {"id":2791,"name":"science","usedCount":0},
 {"id":2800,"name":"health","usedCount":0},
 {"id":951,"name":"insects","usedCount":0},
 {"id":2815,"name":"biology","usedCount":0},
 {"id":2869,"name":"bodies","usedCount":0},
 {"id":578,"name":"shoes","usedCount":0},
 {"id":671,"name":"exercise","usedCount":0},
 {"id":546,"name":"earth","usedCount":0},{"id":565,"name":"test","usedCount":0},
 {"id":577,"name":"rain","usedCount":0},
 {"id":941,"name":"weather","usedCount":0},{"id":3081,"name":"fun in the sun","usedCount":0},{"id":685,"name":"sailing","usedCount":0}]}

In the returned topic list, find the name of the topic that interests you.

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NOTE:
The topic name will display within the name parameter of the returned results.

Note, to the left of the the topic name, at the beginning of the returned information, there is the id parameter. The integer (number) displayed within id is the topicId of the topic you found in step 2.