Least Common Multiple (LCM) of 129 and 162
The least common multiple (LCM) of 129 and 162 is 6966.
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 162?
First, calculate the GCD of 129 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 162 = 0 remainder 129 |
| 2 | 162 ÷ 129 = 1 remainder 33 |
| 3 | 129 ÷ 33 = 3 remainder 30 |
| 4 | 33 ÷ 30 = 1 remainder 3 |
| 5 | 30 ÷ 3 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 141 | 23124 |
| 40 and 149 | 5960 |
| 114 and 36 | 684 |
| 192 and 54 | 1728 |
| 33 and 122 | 4026 |