Least Common Multiple (LCM) of 157 and 129
The least common multiple (LCM) of 157 and 129 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 157 and 129?
First, calculate the GCD of 157 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 157 ÷ 129 = 1 remainder 28 |
| 2 | 129 ÷ 28 = 4 remainder 17 |
| 3 | 28 ÷ 17 = 1 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 108 | 432 |
| 158 and 49 | 7742 |
| 77 and 60 | 4620 |
| 170 and 18 | 1530 |
| 133 and 174 | 23142 |