Least Common Multiple (LCM) of 19 and 122
The least common multiple (LCM) of 19 and 122 is 2318.
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 19 and 122?
First, calculate the GCD of 19 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 122 = 0 remainder 19 |
| 2 | 122 ÷ 19 = 6 remainder 8 |
| 3 | 19 ÷ 8 = 2 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 12 | 60 |
| 55 and 129 | 7095 |
| 185 and 82 | 15170 |
| 128 and 30 | 1920 |
| 141 and 160 | 22560 |