Gwen and Preston are fishermen who, by coincidence, caught the same number of fish this week. Gwen caught fish in nets that hold 46 fish, while Preston caught fish in nets that hold 41 fish. What is the minimum number of fish each must have caught?

To solve this problem, we need to find the least common multiple (LCM) of the numbers 46 and 41, because the LCM will give us the smallest number that is a multiple of both numbers. This is the minimum number of fish each person could have caught.

Step 1: Write down the multiples of 46 and 41.

Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460, 506, 552, 598, 644, 690, 736, 782, 828, 874, 920, 966, 1012, 1058, 1104, 1140, 1186, 1232, 1278, 1324, 1370, 1416, 1462, 1508, 1554, 1600, 1646, 1692, 1738, 1784, 1830, 1876, 1922, 1968, 2014, 2060, 2106, 2152, 2198, 2244, 2290, 2336, 2382, 2428, 2474, 2520, 2566, 2612, 2658, 2704, 2750, 2796, 2842, 2888, 2934, 2980, 3026, 3072, 3118, 3164, 3210, 3256, 3302, 3348, 3394, 3440, 3486, 3532,

To solve this problem, we need to find the least common multiple (LCM) of the numbers 46 and 41, because the LCM will give us the smallest number that is a multiple of both numbers. This is the minimum number of fish each person could have caught.

Step 1: Write down the multiples of 46 and 41.

Multiples of 46: 46, 92, 138, 184, 230, 276, 322, 368, 414, 460, 506, 552, 598, 644, 690, 736, 782, 828, 874, 920, 966, 1012, 1058, 1104, 1150, 1196, 1242, 1288, 1334, 1380, 1426, 1472, 1518, 1564, 1610, 1656, 1702, 1748, 1794, 1840, 1886, 1932, 1978, 2024, 2070, 2116, 2162, 2208, 2254, 2300, 2346, 2392, 2438, 2484, 2530, 2576, 2622, 2668, 2714, 2760, 2806, 2852, 2898, 2944, 2990, 3036, 3082, 3128, 3174, 3220, 3266, 3312, 3358, 3404, 3450, 3496, 3542, 3588, 3634, 3680, 3726, 3772, 3818, 3864, 3910, 3956, 4002, 4048, 4094, 4140, 4186, 4232, 4278, 4324, 4370, 4416, 4462, 4508, 4554, 4600, 4646, 4692, 4738, 4784, 4830, 4876, 4922, 4968, 5014, 5060, 5106, 5152, 5198, 5244, 5290, 5336, 5382, 5428, 5474, 5520, 5566, 5612, 5658, 5704, 5750, 5796, 5842, 5888, 5934, 5980, 6026, 6072, 6118, 6164, 6210, 6256, 6302, 6348, 6394, 6440, 6486, 6532, 6578, 6624, 6670, 6716, 6762, 6808, 6854, 6900, 6946, 6992, 7038, 7084, 7130, 7176, 7222, 7268, 7314, 7360, 7406, 7452, 7498, 7544, 7590, 7636, 7682, 7728, 7774, 7820, 7866, 7912, 7958, 8004, 8050, 8096, 8142, 8188, 8234, 8280, 8326, 8372, 8418, 8464, 8510, 8556, 8602, 8648, 8694, 8740, 8786, 8832, 8878, 8924, 8970, 9016, 9062, 9108, 9154, 9200, 9246, 9292, 9338, 9384, 9430, 9476, 9522, 9568, 9614, 9660, 9706, 9752, 9798, 9844, 9890, 9936, 9982, 10028, 10074, 10120, 10166, 10212, 10258, 10304, 10350, 10396, 10442, 10488, 10534, 10580, 10626, 10672, 10718, 10764, 10810, 10856, 10902, 10948, 10994, 11040, 11086, 11132, 11178, 11224, 11270, 11316, 11362, 11408, 11454, 11500, 11546, 11592, 11638, 11684, 11730, 11776, 11822, 11868, 11914, 11960, 12006, 12052, 12098, 12144, 12190, 12236, 12282, 12328, 12374, 12420, 12466, 12512, 12558, 12604, 12650, 12696, 12742, 12788, 12834, 12880, 12926, 12972, 13018, 13064, 13110, 13156, 13202, 13248, 13294, 13340, 13386, 13432, 13478, 13524, 13570, 13616, 13662, 13708, 13754, 13800, 13846, 13892, 13938, 13984, 14030, 14076, 14122, 14168, 14214, 14260, 14306, 14352, 14398, 14444, 14490, 14536, 14582, 14628, 14674, 14720, 14766, 14812, 14858, 14904, 14950, 14996, 15042, 15088, 15134, 15180, 15226, 15272, 15318, 15364, 15410, 15456, 15502, 15548, 15594, 15640, 15686, 15732, 15778, 15824, 15870, 15916, 15962, 16008, 16054, 16100, 16146, 16192, 16238, 16284, 16330, 16376, 16422, 16468, 16514, 16560, 16606, 16652, 16698, 16744, 16790, 16836, 16882, 16928, 16974, 17020, 17066, 17112, 17158, 17204, 17250, 17296, 17342, 17388, 17434, 17480, 17526, 17572, 17618, 17664, 17710, 17756, 17802, 17848, 17894, 17940, 17986, 18032, 18078, 18124, 18170, 18216, 18262, 18308, 18354, 18400, 18446, 18492, 18538, 18584, 18630, 18676, 18722, 18768, 18814, 18860, 18906, 18952, 18998, 19044, 19090, 19136, 19182, 19228, 19274, 19320, 19366, 19412, 19458, 19504, 19550, 19596, 19642, 19688, 19734, 19780, 19826, 19872, 19918, 19964, 20010, 20056, 20102, 20148, 20194, 20240, 20286, 20332, 20378, 20424, 20470, 20516, 20562, 20608, 20654, 20700, 20746, 20792, 20838, 20884, 20930, 20976, 21022, 21068, 21114, 21160, 21206, 21252, 21298, 21344, 21390, 21436, 21482, 21528, 21574, 21620, 21666, 21712, 21758, 21804, 21850, 21896, 21942, 21988, 22034, 22080, 22126, 22172,