Least Common Multiple (LCM) of 101 and 129
The least common multiple (LCM) of 101 and 129 is 13029.
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 101 and 129?
First, calculate the GCD of 101 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 129 = 0 remainder 101 |
| 2 | 129 ÷ 101 = 1 remainder 28 |
| 3 | 101 ÷ 28 = 3 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 178 | 1246 |
| 63 and 51 | 1071 |
| 144 and 63 | 1008 |
| 140 and 49 | 980 |
| 130 and 60 | 780 |