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 |
|---|---|
| 52 and 135 | 7020 |
| 71 and 19 | 1349 |
| 12 and 132 | 132 |
| 170 and 102 | 510 |
| 35 and 167 | 5845 |