Least Common Multiple (LCM) of 100 and 129
The least common multiple (LCM) of 100 and 129 is 12900.
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 100 and 129?
First, calculate the GCD of 100 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 129 = 0 remainder 100 |
| 2 | 129 ÷ 100 = 1 remainder 29 |
| 3 | 100 ÷ 29 = 3 remainder 13 |
| 4 | 29 ÷ 13 = 2 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 186 | 11346 |
| 157 and 109 | 17113 |
| 59 and 153 | 9027 |
| 200 and 72 | 1800 |
| 134 and 161 | 21574 |