Least Common Multiple (LCM) of 121 and 195
The least common multiple (LCM) of 121 and 195 is 23595.
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 121 and 195?
First, calculate the GCD of 121 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 195 = 0 remainder 121 |
| 2 | 195 ÷ 121 = 1 remainder 74 |
| 3 | 121 ÷ 74 = 1 remainder 47 |
| 4 | 74 ÷ 47 = 1 remainder 27 |
| 5 | 47 ÷ 27 = 1 remainder 20 |
| 6 | 27 ÷ 20 = 1 remainder 7 |
| 7 | 20 ÷ 7 = 2 remainder 6 |
| 8 | 7 ÷ 6 = 1 remainder 1 |
| 9 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 82 | 574 |
| 51 and 17 | 51 |
| 19 and 21 | 399 |
| 115 and 186 | 21390 |
| 40 and 61 | 2440 |