Least Common Multiple (LCM) of 108 and 38
The least common multiple (LCM) of 108 and 38 is 2052.
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 108 and 38?
First, calculate the GCD of 108 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 38 = 2 remainder 32 |
| 2 | 38 ÷ 32 = 1 remainder 6 |
| 3 | 32 ÷ 6 = 5 remainder 2 |
| 4 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 62 | 5394 |
| 155 and 196 | 30380 |
| 128 and 22 | 1408 |
| 96 and 95 | 9120 |
| 120 and 49 | 5880 |