Least Common Multiple (LCM) of 138 and 108
The least common multiple (LCM) of 138 and 108 is 2484.
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 138 and 108?
First, calculate the GCD of 138 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 108 = 1 remainder 30 |
| 2 | 108 ÷ 30 = 3 remainder 18 |
| 3 | 30 ÷ 18 = 1 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 92 | 2760 |
| 34 and 24 | 408 |
| 104 and 155 | 16120 |
| 32 and 140 | 1120 |
| 10 and 135 | 270 |