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

The multipliers of 38 are: 38, 76, 114, 152, 190, 228, 266, 304, 342, 380, 418, 456, 494, 532, 570, 608, 646, 684, 722, 760, 798, 836, 874, 912, 950, 988, 1026, . . .

The multipliers of 52 are: 52, 104, 156, 208, 260, 312, 364, 416, 468, 520, 572, 624, 676, 728, 780, 832, 884, 936, 988, 1040, . . .

We can see that:

LCM( 38, 52 ) = 988

This solution can be visualized using a Venn diagram.

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