Least Common Multiple (LCM) of 123 and 109
The least common multiple (LCM) of 123 and 109 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 123 and 109?
First, calculate the GCD of 123 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 109 = 1 remainder 14 |
| 2 | 109 ÷ 14 = 7 remainder 11 |
| 3 | 14 ÷ 11 = 1 remainder 3 |
| 4 | 11 ÷ 3 = 3 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 157 | 23079 |
| 142 and 155 | 22010 |
| 83 and 150 | 12450 |
| 185 and 144 | 26640 |
| 186 and 169 | 31434 |