Least Common Multiple (LCM) of 195 and 119
The least common multiple (LCM) of 195 and 119 is 23205.
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 119?
First, calculate the GCD of 195 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 119 = 1 remainder 76 |
| 2 | 119 ÷ 76 = 1 remainder 43 |
| 3 | 76 ÷ 43 = 1 remainder 33 |
| 4 | 43 ÷ 33 = 1 remainder 10 |
| 5 | 33 ÷ 10 = 3 remainder 3 |
| 6 | 10 ÷ 3 = 3 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 172 | 7740 |
| 157 and 36 | 5652 |
| 113 and 48 | 5424 |
| 165 and 188 | 31020 |
| 99 and 79 | 7821 |