Least Common Multiple (LCM) of 36 and 108
The least common multiple (LCM) of 36 and 108 is 108.
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 108?
First, calculate the GCD of 36 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 108 = 0 remainder 36 |
| 2 | 108 ÷ 36 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 125 and 107 | 13375 |
| 51 and 187 | 561 |
| 23 and 197 | 4531 |
| 83 and 106 | 8798 |
| 180 and 10 | 180 |