What is a number between 364 and 384 that is a multiple of both 3 and 7

378

Step-by-step explanation:

It will also be a multiple of 21.

As it is divisible by 3 the first possibility is 366 so:-

364 + n = 21m

where n = 2,5,8,11,14 ...

Trying each number in turn we get:-

364 + 14 = 21m

21m = 378

m = 18

so the answer is 378