Multiple Mystery

Number Theory Level 5

\[\text{lcm} (a, b) = \text{lcm}(b, c) =\text{lcm}(c, a) = a + b + c -1\]

Let \(a < b < c\) be the positive integers satisfying the constraint above.

If \(29\) is the largest number that can not be represented as the sum of \(a, b, c\) multiples, also known as Frobenius number, what is the value of \(\text{lcm}(a-1, b-1, c-1)\)?

Note: \(\text{lcm} (\cdot) \) denotes the least common multiple function.


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