Least Common Multiple (LCM) of 122 and 157
The least common multiple (LCM) of 122 and 157 is 19154.
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 157?
First, calculate the GCD of 122 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 157 = 0 remainder 122 |
| 2 | 157 ÷ 122 = 1 remainder 35 |
| 3 | 122 ÷ 35 = 3 remainder 17 |
| 4 | 35 ÷ 17 = 2 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 75 | 14025 |
| 89 and 45 | 4005 |
| 51 and 132 | 2244 |
| 16 and 103 | 1648 |
| 131 and 81 | 10611 |