Least Common Multiple (LCM) of 195 and 138
The least common multiple (LCM) of 195 and 138 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 195 and 138?
First, calculate the GCD of 195 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 138 = 1 remainder 57 |
| 2 | 138 ÷ 57 = 2 remainder 24 |
| 3 | 57 ÷ 24 = 2 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 38 | 342 |
| 82 and 70 | 2870 |
| 165 and 98 | 16170 |
| 95 and 79 | 7505 |
| 130 and 182 | 910 |