In general, the least common multiple (lcm) is the smallest multiple that a set of terms have in common.
Example 1: 36x7 is the least common multiple of 12x7 and 18x3.
Example 2: 36x5y4z is the least common multiple of 12x5y2z, 6x4y3z and 18x3y4.
Example 3: 360x50y4z is a common multiple of 12x5y2z, 6x4y3z and 18x3y4, but it is NOT the LEAST common multiple.
Example 4: 12x50y2z is a NOT a COMMON multiple of 12x5y2z, 6x4y3z and 18x3y4. It is therefore not the LEAST common multiple.
Example 5: 7xy is NOT a multiple of 12x5y2z, 6x4y3z or 18x3y4. It is therefore not the least common multiple.
The least common multiple (lcm) is the smallest natural number that is a multiple of two or more given natural numbers.
Example 1: 36 is the least common multiple of 12 and 18.
Example 2: 360 is a common multiple of 12 and 18, but it is NOT the LEAST common multiple.
Example 3: 24 is NOT a COMMON multiple of 12 and 18. It is therefore not the GREATEST common multiple.
Example 4: 20 is NOT a multiple of 12 or 18. It is therefore not the greatest common multiple.