Least Common Multiple (LCM) of 107 and 195
The least common multiple (LCM) of 107 and 195 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 107 and 195?
First, calculate the GCD of 107 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 195 = 0 remainder 107 |
| 2 | 195 ÷ 107 = 1 remainder 88 |
| 3 | 107 ÷ 88 = 1 remainder 19 |
| 4 | 88 ÷ 19 = 4 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 158 | 11218 |
| 111 and 84 | 3108 |
| 114 and 78 | 1482 |
| 45 and 134 | 6030 |
| 123 and 138 | 5658 |