A number leaves remainder 3 when divided by 7 and remainder 3 when divided by 5. The smallest such number above 3 is:

1. If a number leaves the same remainder 3 with both divisors, then the number minus 3 is divisible by both. 2. So the number minus 3 must be a common multiple of 7 and 5. 3. Since 7 and 5 share no prime factor, their LCM is 7 x 5 = 35. 4. The smallest such value above 3 is therefore 35 + 3 = 38. 5. 33 and 31 are not 3 more than a multiple of 35, and 35 itself leaves remainder 0 with 5. _Source: syllabus Maths, Ch 1 'Real Numbers', S1.2 The Fundamental Theorem of Arithmetic_