Least Common Multiple (LCM) of 106 and 123
The least common multiple (LCM) of 106 and 123 is 13038.
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 106 and 123?
First, calculate the GCD of 106 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 123 = 0 remainder 106 |
| 2 | 123 ÷ 106 = 1 remainder 17 |
| 3 | 106 ÷ 17 = 6 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 68 | 612 |
| 11 and 97 | 1067 |
| 78 and 167 | 13026 |
| 112 and 55 | 6160 |
| 45 and 84 | 1260 |