Least Common Multiple (LCM) of 195 and 107
The least common multiple (LCM) of 195 and 107 is 20865.
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 107?
First, calculate the GCD of 195 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 107 = 1 remainder 88 |
| 2 | 107 ÷ 88 = 1 remainder 19 |
| 3 | 88 ÷ 19 = 4 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 144 | 3600 |
| 186 and 175 | 32550 |
| 122 and 34 | 2074 |
| 156 and 189 | 9828 |
| 52 and 24 | 312 |