Question

LCM of 51,187,153,165
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Answer 1

Answer:

8415 is the LCM

Step-by-step explanation:

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Answer 2

Answer:

8415

Step-by-step explanation:

Process 1:-

#1 Make a list of the multiples of each number, until you find the first common multiple of all the numbers:

• Multiples of 51: 51, 102, 153, 204, 255, 306, 357, 408, 459, ..., 3978, 4029, 4080, 4131, 4182, 4233, 4284, 4335, 4386, 4437, ..., 8160, 8211, 8262, 8313, 8364, 8415, 8466, 8517, 8568, 8619 ...

• Multiples of 187: 187, 374, 561, 748, 935, 1122, 1309, 1496, 1683, 1870, 2057, 2244, 2431, 2618, 2805, 2992, 3179, 3366, 3553, 3740, 3927, 4114, 4301, 4488, 4675, 4862, 5049, 5236, 5423, 5610, 5797, 5984, 6171, 6358, 6545, 6732, 6919, 7106, 7293, 7480, 7667, 7854, 8041, 8228, 8415, 8602, 8789, 8976 ...

• Multiples of 153: 153, 306, 459, 612, 765, 918, 1071, 1224, 1377, 1530, 1683, 1836, 1989, 2142, 2295, 2448, 2601, 2754, 2907, 3060, 3213, 3366, 3519, 3672, 3825, 3978, 4131, 4284, 4437, 4590, 4743, 4896, 5049, 5202, 5355, 5508, 5661, 5814, 5967, 6120, 6273, 6426, 6579, 6732, 6885, 7038, 7191, 7344, 7497, 7650, 7803, 7956, 8109, 8262, 8415, 8568, 8721, 8874 ...

• Multiples of 165: 165, 330, 495, 660, 825, 990, 1155, 1320, 1485, 1650, 1815, 1980, 2145, 2310, 2475, 2640, 2805, 2970, 3135, 3300, 3465, 3630, 3795, 3960, 4125, 4290, 4455, 4620, 4785, 4950, 5115, 5280, 5445, 5610, 5775, 5940, 6105, 6270, 6435, 6600, 6765, 6930, 7095, 7260, 7425, 7590, 7755, 7920, 8085, 8250, 8415, 8580, 8745, 8910 ...

Process 2 :-

#1 Write down all of the numbers as a product of their prime factors:

• Prime factorisation of 51:

3 * 17 = 31 * 171

• Prime factorisation of 187:

11 * 17 = 111 * 171

• Prime factorisation of 153:

3 * 3 * 17 = 32 * 171

• Prime factorisation of 165:

3 * 5 * 11 = 31 * 51 * 111

#2 Find highest power of each prime number:

32 , 171 , 111 , 51

#3 Multiply these values together:

32 * 171 * 111 * 51 = 8415

Thus,

LCM(51,187,153,165) = 8415

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