Least Common Multiple (LCM) of 129 and 157
The least common multiple (LCM) of 129 and 157 is 20253.
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 129 and 157?
First, calculate the GCD of 129 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 157 = 0 remainder 129 |
| 2 | 157 ÷ 129 = 1 remainder 28 |
| 3 | 129 ÷ 28 = 4 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 46 | 5658 |
| 185 and 130 | 4810 |
| 26 and 21 | 546 |
| 170 and 116 | 9860 |
| 167 and 194 | 32398 |