Least Common Multiple (LCM) of 109 and 123
The least common multiple (LCM) of 109 and 123 is 13407.
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 109 and 123?
First, calculate the GCD of 109 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 123 = 0 remainder 109 |
| 2 | 123 ÷ 109 = 1 remainder 14 |
| 3 | 109 ÷ 14 = 7 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 141 | 4089 |
| 193 and 102 | 19686 |
| 152 and 105 | 15960 |
| 23 and 142 | 3266 |
| 71 and 148 | 10508 |