Least common multiple of 26,39 using prime factorization

26 is a multiple of 2 but 39 isn't

39 is a multiple of 3 but 26 isn't

Dividng by the next three prime numbers, neither 26 nor 39 is a multiple of 5, 7, or 11

Moving up to the sixth prime number (13), we see that BOTH 26 and 39 are divisible by 13.  26 = 2 * 13 and 39 = 3 * 13 and 13 is the lowest common multiple of 26 and 39.