The LCM of several integers can be found by writing the prime factorization of each of the integers in question and then taking the least number necessary of each prime factor.
Ex.
Let’s find the LCM of 12, 18, and 24:
12 = 2 x 6 = 2 x 2 x 3
18 = 2 x 9 = 2 x 3 x 3
24 = 2 x 12 = 2 x 3 x 4 = 2 x 2 x 2 x 3
Thus,
18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
12 has two prime factors of 2, 18 has one prime factor of 2, and 24 has three prime factors of 2. So the minimum number of prime factors of 2 needed is 3.
12 has one prime factor of 3, 18 has two prime factors of 3, and 24 has one prime factor of 3. So the minimum number of prime factors of 3 needed is 2.
So the LCM of 12, 18, and 24 is 2 x 2 x 2 x 3 x 3 = 2
^{3} x 3
^{2} = 8 x 9 = 72.