Least Common Multiple (LCM) of 36 and 129
The least common multiple (LCM) of 36 and 129 is 1548.
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 36 and 129?
First, calculate the GCD of 36 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 129 = 0 remainder 36 |
| 2 | 129 ÷ 36 = 3 remainder 21 |
| 3 | 36 ÷ 21 = 1 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 28 | 2492 |
| 15 and 10 | 30 |
| 57 and 192 | 3648 |
| 111 and 37 | 111 |
| 121 and 137 | 16577 |