To find the largest perfect square factor of 11280, we need to factorize 11280 into its prime factors, which are 2, 2, 2, 3, 5, 11, and 17. To find the perfect square factor, we pair up the prime factors into their squares, which gives us 2^2 and 3^2. Therefore, the largest perfect square factor of 11280 is 2^2 * 3^2 = 36.
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They both go into all multiples of their LCM (which is 120). The first 100 are: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000, 9120, 9240, 9360, 9480, 9600, 9720, 9840, 9960, 10080, 10200, 10320, 10440, 10560, 10680, 10800, 10920, 11040, 11160, 11280, 11400, 11520, 11640, 11760, 11880, 12000, ...
There is no one common multiple of 24 and 30. All multiples of the lowest common multiple are multiples of 24 and 30.The lcm of 24 and 30 is 120.Thus the common multiples of 24 and 30 are:120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680, 1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000, 3120, 3240, 3360, 3480, 3600, 3720, 3840, 3960, 4080, 4200, 4320, 4440, 4560, 4680, 4800, 4920, 5040, 5160, 5280, 5400, 5520, 5640, 5760, 5880, 6000, 6120, 6240, 6360, 6480, 6600, 6720, 6840, 6960, 7080, 7200, 7320, 7440, 7560, 7680, 7800, 7920, 8040, 8160, 8280, 8400, 8520, 8640, 8760, 8880, 9000, 9120, 9240, 9360, 9480, 9600, 9720, 9840, 9960, 10080, 10200, 10320, 10440, 10560, 10680, 10800, 10920, 11040, 11160, 11280, 11400, 11520, 11640, 11760, 11880, 12000, ...