Find Least Common Multiple of 56, 64 and 88 by listing out the factors.
Answer
LCM( 56, 64, 88 ) = 4928
Explanation
Write down multiples of each number until you find the first common multiple:
The multipliers of 56 are: 56, 112, 168, 224, 280, 336, 392, 448, 504, 560, 616, 672, 728, 784, 840, 896, 952, 1008, 1064, 1120, 1176, 1232, 1288, 1344, 1400, 1456, 1512, 1568, 1624, 1680, 1736, 1792, 1848, 1904, 1960, 2016, 2072, 2128, 2184, 2240, 2296, 2352, 2408, 2464, 2520, 2576, 2632, 2688, 2744, 2800, 2856, 2912, 2968, 3024, 3080, 3136, 3192, 3248, 3304, 3360, 3416, 3472, 3528, 3584, 3640, 3696, 3752, 3808, 3864, 3920, 3976, 4032, 4088, 4144, 4200, 4256, 4312, 4368, 4424, 4480, 4536, 4592, 4648, 4704, 4760, 4816, 4872, 4928, 4984, . . .
The multipliers of 64 are: 64, 128, 192, 256, 320, 384, 448, 512, 576, 640, 704, 768, 832, 896, 960, 1024, 1088, 1152, 1216, 1280, 1344, 1408, 1472, 1536, 1600, 1664, 1728, 1792, 1856, 1920, 1984, 2048, 2112, 2176, 2240, 2304, 2368, 2432, 2496, 2560, 2624, 2688, 2752, 2816, 2880, 2944, 3008, 3072, 3136, 3200, 3264, 3328, 3392, 3456, 3520, 3584, 3648, 3712, 3776, 3840, 3904, 3968, 4032, 4096, 4160, 4224, 4288, 4352, 4416, 4480, 4544, 4608, 4672, 4736, 4800, 4864, 4928, 4992, . . .
The multipliers of 88 are: 88, 176, 264, 352, 440, 528, 616, 704, 792, 880, 968, 1056, 1144, 1232, 1320, 1408, 1496, 1584, 1672, 1760, 1848, 1936, 2024, 2112, 2200, 2288, 2376, 2464, 2552, 2640, 2728, 2816, 2904, 2992, 3080, 3168, 3256, 3344, 3432, 3520, 3608, 3696, 3784, 3872, 3960, 4048, 4136, 4224, 4312, 4400, 4488, 4576, 4664, 4752, 4840, 4928, 5016, . . .
We can see that:
LCM( 56, 64, 88 ) = 4928
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.