Least Common Multiple (LCM) of 107 and 123
The least common multiple (LCM) of 107 and 123 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 107 and 123?
First, calculate the GCD of 107 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 123 = 0 remainder 107 |
| 2 | 123 ÷ 107 = 1 remainder 16 |
| 3 | 107 ÷ 16 = 6 remainder 11 |
| 4 | 16 ÷ 11 = 1 remainder 5 |
| 5 | 11 ÷ 5 = 2 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 62 | 186 |
| 113 and 196 | 22148 |
| 195 and 54 | 3510 |
| 109 and 120 | 13080 |
| 188 and 192 | 9024 |