Least Common Multiple (LCM) of 119 and 195
The least common multiple (LCM) of 119 and 195 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 119 and 195?
First, calculate the GCD of 119 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 195 = 0 remainder 119 |
| 2 | 195 ÷ 119 = 1 remainder 76 |
| 3 | 119 ÷ 76 = 1 remainder 43 |
| 4 | 76 ÷ 43 = 1 remainder 33 |
| 5 | 43 ÷ 33 = 1 remainder 10 |
| 6 | 33 ÷ 10 = 3 remainder 3 |
| 7 | 10 ÷ 3 = 3 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 117 | 5148 |
| 178 and 95 | 16910 |
| 137 and 110 | 15070 |
| 71 and 80 | 5680 |
| 143 and 39 | 429 |