Least Common Multiple (LCM) of 118 and 129
The least common multiple (LCM) of 118 and 129 is 15222.
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 118 and 129?
First, calculate the GCD of 118 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 129 = 0 remainder 118 |
| 2 | 129 ÷ 118 = 1 remainder 11 |
| 3 | 118 ÷ 11 = 10 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 106 | 11130 |
| 24 and 56 | 168 |
| 150 and 183 | 9150 |
| 160 and 107 | 17120 |
| 33 and 187 | 561 |