Least Common Multiple (LCM) of 123 and 107
The least common multiple (LCM) of 123 and 107 is 13161.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 123 and 107?
First, calculate the GCD of 123 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 107 = 1 remainder 16 |
| 2 | 107 ÷ 16 = 6 remainder 11 |
| 3 | 16 ÷ 11 = 1 remainder 5 |
| 4 | 11 ÷ 5 = 2 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 67 | 6700 |
| 41 and 56 | 2296 |
| 62 and 124 | 124 |
| 10 and 92 | 460 |
| 152 and 81 | 12312 |