# 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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