Least Common Multiple (LCM) of 129 and 170
The least common multiple (LCM) of 129 and 170 is 21930.
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 170?
First, calculate the GCD of 129 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 170 = 0 remainder 129 |
| 2 | 170 ÷ 129 = 1 remainder 41 |
| 3 | 129 ÷ 41 = 3 remainder 6 |
| 4 | 41 ÷ 6 = 6 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 138 | 27186 |
| 53 and 181 | 9593 |
| 179 and 162 | 28998 |
| 128 and 177 | 22656 |
| 153 and 94 | 14382 |