Least Common Multiple (LCM) of 122 and 159
The least common multiple (LCM) of 122 and 159 is 19398.
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 122 and 159?
First, calculate the GCD of 122 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 159 = 0 remainder 122 |
| 2 | 159 ÷ 122 = 1 remainder 37 |
| 3 | 122 ÷ 37 = 3 remainder 11 |
| 4 | 37 ÷ 11 = 3 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 47 and 104 | 4888 |
| 112 and 190 | 10640 |
| 51 and 67 | 3417 |
| 62 and 138 | 4278 |
| 186 and 157 | 29202 |