Least Common Multiple (LCM) of 129 and 169
The least common multiple (LCM) of 129 and 169 is 21801.
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 169?
First, calculate the GCD of 129 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 169 = 0 remainder 129 |
| 2 | 169 ÷ 129 = 1 remainder 40 |
| 3 | 129 ÷ 40 = 3 remainder 9 |
| 4 | 40 ÷ 9 = 4 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 19 | 3743 |
| 108 and 117 | 1404 |
| 152 and 111 | 16872 |
| 171 and 150 | 8550 |
| 185 and 106 | 19610 |