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

The multipliers of 45 are: 45, 90, . . .

The multipliers of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, . . .

We can see that:

LCM( 45, 3 ) = 45

This solution can be visualized using a Venn diagram.

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