What is the LCM of 3, 7, and 2?
The prime factors of 3 are 3, the prime factors of 7 are 7, and the prime factors of 2 are 2. To find the LCM, we need to take the highest power of each prime factor that appears in any of the numbers. Therefore, the LCM of 3, 7, and 2 is 3 x 7 x 2 = 42.
Alternatively, we can list the multiples of each number until we find the smallest multiple that they all have in common.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42...
Multiples of 7: 7, 14, 21, 28, 35, 42...
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42...
Therefore, the LCM is 42.