Least Common Multiple (LCM) of 138 and 195
The least common multiple (LCM) of 138 and 195 is 8970.
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 195?
First, calculate the GCD of 138 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 195 = 0 remainder 138 |
| 2 | 195 ÷ 138 = 1 remainder 57 |
| 3 | 138 ÷ 57 = 2 remainder 24 |
| 4 | 57 ÷ 24 = 2 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 112 | 2576 |
| 48 and 141 | 2256 |
| 16 and 154 | 1232 |
| 75 and 71 | 5325 |
| 160 and 55 | 1760 |