If x, y, z are positive integers satisfying 13x = 17y = 19z, find the minimum value of x + y + z.
Let's find the LCM of them all
\(13(13,26,39,52,65,78,91,104,117,130,143,156,169,182,195,208,221,234,247,260,273,286,299,312,325,338,351,364,377,390,403,416,429,442,455,468,481,494,507,520,533,546,559,572,585,598,611,624,637)\)
\(17(17,34,51,68,85,102,119,136,153,170,187,204,221,238,255,272,289,306,323,340,357,374,391,408,425,442,459,476,493,510,527,544,561,578,595,612,629,646,663,680,697,714,731,748,765,782,799,816,833) \)
\(19(19,38,57,76,95,114,133,152,171,190,209,228,247,266,285,304,323,342,361,380,399,418,437,456,475,494,513,532,551,570,589,608,627,646,665,684,703,722,741,760,779,798,817,836,855,874,893,912,931)\)
There is no LCM for them at least what one can write in an exam.........