Write down multiples of each number until you find the first common multiple:

The multipliers of 299 are: 299, 598, 897, 1196, 1495, 1794, 2093, 2392, 2691, 2990, 3289, 3588, 3887, 4186, 4485, 4784, 5083, 5382, 5681, 5980, . . .

The multipliers of 247 are: 247, 494, 741, 988, 1235, 1482, 1729, 1976, 2223, 2470, 2717, 2964, 3211, 3458, 3705, 3952, 4199, 4446, 4693, 4940, 5187, 5434, 5681, 5928, . . .

We can see that:

LCM( 299, 247 ) = 5681

This solution can be visualized using a Venn diagram.

The LCM is equal to the product of all the numbers on the diagram.