Least Common Multiple (LCM) of 90 and 129
The least common multiple (LCM) of 90 and 129 is 3870.
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 90 and 129?
First, calculate the GCD of 90 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 129 = 0 remainder 90 |
| 2 | 129 ÷ 90 = 1 remainder 39 |
| 3 | 90 ÷ 39 = 2 remainder 12 |
| 4 | 39 ÷ 12 = 3 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 12 | 204 |
| 168 and 196 | 1176 |
| 173 and 32 | 5536 |
| 90 and 53 | 4770 |
| 49 and 115 | 5635 |