To be divided by 6 and 9, the number must be divisible by the lcm of 6 and 9 = 18.
The solution is 4 digit multiples of 18:
1000 ÷ 18 = 555/9 ⇒ first 4 digit multiple of 18 is 18 x 56 = 1008
9999 ÷ 18 = 5551/2 ⇒ last 4 digit multiple of 18 is 18 x 555 = 9990
Which means the 500 4-digit numbers divisible by 6 and 9 are:
1008, 1026, 1044, 1062, 1080, 1098, 1116, 1134, 1152, 1170, 1188, 1206, 1224, 1242, 1260, 1278, 1296, 1314, 1332, 1350, 1368, 1386, 1404, 1422, 1440, 1458, 1476, 1494, 1512, 1530, 1548, 1566, 1584, 1602, 1620, 1638, 1656, 1674, 1692, 1710, 1728, 1746, 1764, 1782, 1800, 1818, 1836, 1854, 1872, 1890, 1908, 1926, 1944, 1962, 1980, 1998, 2016, 2034, 2052, 2070, 2088, 2106, 2124, 2142, 2160, 2178, 2196, 2214, 2232, 2250, 2268, 2286, 2304, 2322, 2340, 2358, 2376, 2394, 2412, 2430, 2448, 2466, 2484, 2502, 2520, 2538, 2556, 2574, 2592, 2610, 2628, 2646, 2664, 2682, 2700, 2718, 2736, 2754, 2772, 2790, 2808, 2826, 2844, 2862, 2880, 2898, 2916, 2934, 2952, 2970, 2988, 3006, 3024, 3042, 3060, 3078, 3096, 3114, 3132, 3150, 3168, 3186, 3204, 3222, 3240, 3258, 3276, 3294, 3312, 3330, 3348, 3366, 3384, 3402, 3420, 3438, 3456, 3474, 3492, 3510, 3528, 3546, 3564, 3582, 3600, 3618, 3636, 3654, 3672, 3690, 3708, 3726, 3744, 3762, 3780, 3798, 3816, 3834, 3852, 3870, 3888, 3906, 3924, 3942, 3960, 3978, 3996, 4014, 4032, 4050, 4068, 4086, 4104, 4122, 4140, 4158, 4176, 4194, 4212, 4230, 4248, 4266, 4284, 4302, 4320, 4338, 4356, 4374, 4392, 4410, 4428, 4446, 4464, 4482, 4500, 4518, 4536, 4554, 4572, 4590, 4608, 4626, 4644, 4662, 4680, 4698, 4716, 4734, 4752, 4770, 4788, 4806, 4824, 4842, 4860, 4878, 4896, 4914, 4932, 4950, 4968, 4986, 5004, 5022, 5040, 5058, 5076, 5094, 5112, 5130, 5148, 5166, 5184, 5202, 5220, 5238, 5256, 5274, 5292, 5310, 5328, 5346, 5364, 5382, 5400, 5418, 5436, 5454, 5472, 5490, 5508, 5526, 5544, 5562, 5580, 5598, 5616, 5634, 5652, 5670, 5688, 5706, 5724, 5742, 5760, 5778, 5796, 5814, 5832, 5850, 5868, 5886, 5904, 5922, 5940, 5958, 5976, 5994, 6012, 6030, 6048, 6066, 6084, 6102, 6120, 6138, 6156, 6174, 6192, 6210, 6228, 6246, 6264, 6282, 6300, 6318, 6336, 6354, 6372, 6390, 6408, 6426, 6444, 6462, 6480, 6498, 6516, 6534, 6552, 6570, 6588, 6606, 6624, 6642, 6660, 6678, 6696, 6714, 6732, 6750, 6768, 6786, 6804, 6822, 6840, 6858, 6876, 6894, 6912, 6930, 6948, 6966, 6984, 7002, 7020, 7038, 7056, 7074, 7092, 7110, 7128, 7146, 7164, 7182, 7200, 7218, 7236, 7254, 7272, 7290, 7308, 7326, 7344, 7362, 7380, 7398, 7416, 7434, 7452, 7470, 7488, 7506, 7524, 7542, 7560, 7578, 7596, 7614, 7632, 7650, 7668, 7686, 7704, 7722, 7740, 7758, 7776, 7794, 7812, 7830, 7848, 7866, 7884, 7902, 7920, 7938, 7956, 7974, 7992, 8010, 8028, 8046, 8064, 8082, 8100, 8118, 8136, 8154, 8172, 8190, 8208, 8226, 8244, 8262, 8280, 8298, 8316, 8334, 8352, 8370, 8388, 8406, 8424, 8442, 8460, 8478, 8496, 8514, 8532, 8550, 8568, 8586, 8604, 8622, 8640, 8658, 8676, 8694, 8712, 8730, 8748, 8766, 8784, 8802, 8820, 8838, 8856, 8874, 8892, 8910, 8928, 8946, 8964, 8982, 9000, 9018, 9036, 9054, 9072, 9090, 9108, 9126, 9144, 9162, 9180, 9198, 9216, 9234, 9252, 9270, 9288, 9306, 9324, 9342, 9360, 9378, 9396, 9414, 9432, 9450, 9468, 9486, 9504, 9522, 9540, 9558, 9576, 9594, 9612, 9630, 9648, 9666, 9684, 9702, 9720, 9738, 9756, 9774, 9792, 9810, 9828, 9846, 9864, 9882, 9900, 9918, 9936, 9954, 9972, 9990
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Any number that can be divided by 2 is called an even number. For simplicity, the last digit of an even number must be 0, 2, 4, 6, or 8. The number 32906986 last digit is 6, so it is an even number.
what is the largest three-digit number that is divisible by 4, 5, and 6
6
You can't have a remainder of 6 when you divide by 2! JHC!
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