Find Least Common Multiple of 72, 90 and 81 by listing out the factors.
Answer
LCM( 72, 90, 81 ) = 3240
Explanation
Write down multiples of each number until you find the first common multiple:
The multipliers of 72 are: 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, 792, 864, 936, 1008, 1080, 1152, 1224, 1296, 1368, 1440, 1512, 1584, 1656, 1728, 1800, 1872, 1944, 2016, 2088, 2160, 2232, 2304, 2376, 2448, 2520, 2592, 2664, 2736, 2808, 2880, 2952, 3024, 3096, 3168, 3240, 3312, . . .
The multipliers of 90 are: 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, 990, 1080, 1170, 1260, 1350, 1440, 1530, 1620, 1710, 1800, 1890, 1980, 2070, 2160, 2250, 2340, 2430, 2520, 2610, 2700, 2790, 2880, 2970, 3060, 3150, 3240, 3330, . . .
The multipliers of 81 are: 81, 162, 243, 324, 405, 486, 567, 648, 729, 810, 891, 972, 1053, 1134, 1215, 1296, 1377, 1458, 1539, 1620, 1701, 1782, 1863, 1944, 2025, 2106, 2187, 2268, 2349, 2430, 2511, 2592, 2673, 2754, 2835, 2916, 2997, 3078, 3159, 3240, 3321, . . .
We can see that:
LCM( 72, 90, 81 ) = 3240
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.