Least Common Multiple (LCM) of 129 and 164
The least common multiple (LCM) of 129 and 164 is 21156.
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 164?
First, calculate the GCD of 129 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 164 = 0 remainder 129 |
| 2 | 164 ÷ 129 = 1 remainder 35 |
| 3 | 129 ÷ 35 = 3 remainder 24 |
| 4 | 35 ÷ 24 = 1 remainder 11 |
| 5 | 24 ÷ 11 = 2 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 37 | 3996 |
| 161 and 106 | 17066 |
| 64 and 178 | 5696 |
| 79 and 31 | 2449 |
| 120 and 160 | 480 |