Least Common Multiple (LCM) of 55 and 129
The least common multiple (LCM) of 55 and 129 is 7095.
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 55 and 129?
First, calculate the GCD of 55 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 129 = 0 remainder 55 |
| 2 | 129 ÷ 55 = 2 remainder 19 |
| 3 | 55 ÷ 19 = 2 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 98 | 1862 |
| 193 and 84 | 16212 |
| 167 and 130 | 21710 |
| 186 and 176 | 16368 |
| 159 and 100 | 15900 |