Least Common Multiple (LCM) of 138 and 38
The least common multiple (LCM) of 138 and 38 is 2622.
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 38?
First, calculate the GCD of 138 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 38 = 3 remainder 24 |
| 2 | 38 ÷ 24 = 1 remainder 14 |
| 3 | 24 ÷ 14 = 1 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 14 | 1008 |
| 175 and 139 | 24325 |
| 20 and 33 | 660 |
| 172 and 30 | 2580 |
| 31 and 199 | 6169 |