Find Least Common Multiple of 42, 56 and 64 by listing out the factors.
Answer
LCM( 42, 56, 64 ) = 1344
Explanation
Write down multiples of each number until you find the first common multiple:
The multipliers of 42 are: 42, 84, 126, 168, 210, 252, 294, 336, 378, 420, 462, 504, 546, 588, 630, 672, 714, 756, 798, 840, 882, 924, 966, 1008, 1050, 1092, 1134, 1176, 1218, 1260, 1302, 1344, 1386, . . .
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, . . .
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, . . .
We can see that:
LCM( 42, 56, 64 ) = 1344
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.