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If n is a positive integer such that lcm[5n + 7, 7n + 11] = 5980, find the value of 35n^2 + 104n.
thanks!!

 Aug 1, 2023
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5980 = 2^2 * 5 * 13 * 23


Prime factorizations


92 = 2^2×23 (3 prime factors, 2 distinct)
130 = 2×5×13 (3 distinct prime factors)
LCM(92, 130)==2^2 x 5 x 13 x  23=5980


n==[130 - 11] / 7 ==17


35n^2 + 104n ==[35 * 17^2] + [104 * 17]
==10,115  +  1,768 ==11,883

 Aug 1, 2023

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