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 |
|---|---|
| 110 and 91 | 10010 |
| 198 and 40 | 3960 |
| 144 and 44 | 1584 |
| 78 and 162 | 2106 |
| 182 and 10 | 910 |