The least common multiple, or LCM, is the smallest positive number that two or more integers divide evenly. For 4 and 6, the multiples are 4, 8, 12, 16... and 6, 12, 18... The smallest shared multiple is 12.

The LCM is used to add fractions with different denominators. To add 1/4 and 1/6, you convert both to twelfths: 3/12 + 2/12 = 5/12. Finding the LCM of the denominators makes that possible.

The LCM relates to the greatest common divisor: LCM(a, b) = a × b / GCD(a, b). Prime factorization provides another method: take the highest power of each prime appearing in either number. The concept appears in scheduling, gear ratios, and number theory. It is a basic tool with wide application.

• Smallest number divisible by given integers
• Used to add fractions
• LCM(a,b) = a × b / GCD(a,b)
• Found by prime factorization