Explanation:
we need to find the LCM, the least (or lowest) common multiple, of 3 and 4.
that means the smallest number that can be divided by 3 and by 4 without remainder.
and that is simply in our case 3×4 = 12.
so, every 12th day they will walk to the lake "together" (on the same day).
FYI - formality the LCM is found e.g. by prime factorization.
starting with the smallest prime number (2) both numbers are divided by the prime number, if there is no remainder. the quotient is then again divided by the prime number. if there is a remainder, then the next higher prime number is taken for the division.
this goes on until we get a quotient of 1.
the LCM is then the product of the longest streaks of the products of the same prime numbers.
example LCM of 56 and 50
56 ÷ 2 = 28 (0 remainder)
28 ÷ 2 = 14 (0 remainder)
14 ÷ 2 = 7 (0 remainder)
7 ÷ 2 has a remainder, so the next prime number (3)
7 ÷ 3 has a remainder, so the next prime number (5)
7 ÷ 5 has a remainder, so the next prime number (7)
7 ÷ 7 = 1 finished
50 ÷ 2 = 25 (0 remainder)
25 ÷ 2 has a remainder, so the next prime number (3)
25 ÷ 3 has a remainder, so the next prime number (5)
25 ÷ 5 = 5 (0 remainder)
5 ÷ 5 = 1 finished
the longest streaks of prime number products :
2×2×2 = 8
5×5 = 25
7 = 7
the LCM = 8×25×7 = 1400
please consider, this is NOT 56×50 = 2800.
the LCM is not automatically just the product of both numbers. this product is a common multiple, true, but not always the smallest.
in our case here with 3 and 4
3 ÷ 2 has a remainder, so the next prime number (3)
3 ÷ 3 = 1 finished
4 ÷ 2 = 2 (0 remainder)
2 ÷ 2 = 1 finished
the longest prime number product streaks :
2×2 = 4
3 = 3
the LCM = 4×3 = 12
so, in this case the LCM is the direct product of both numbers.