Least Common Multiple (LCM) of 109 and 122
The least common multiple (LCM) of 109 and 122 is 13298.
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 122?
First, calculate the GCD of 109 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 122 = 0 remainder 109 |
| 2 | 122 ÷ 109 = 1 remainder 13 |
| 3 | 109 ÷ 13 = 8 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 169 | 21632 |
| 82 and 136 | 5576 |
| 156 and 161 | 25116 |
| 115 and 104 | 11960 |
| 91 and 90 | 8190 |