Least Common Multiple (LCM) of 116 and 195
The least common multiple (LCM) of 116 and 195 is 22620.
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 116 and 195?
First, calculate the GCD of 116 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 195 = 0 remainder 116 |
| 2 | 195 ÷ 116 = 1 remainder 79 |
| 3 | 116 ÷ 79 = 1 remainder 37 |
| 4 | 79 ÷ 37 = 2 remainder 5 |
| 5 | 37 ÷ 5 = 7 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 40 | 920 |
| 175 and 56 | 1400 |
| 66 and 169 | 11154 |
| 95 and 40 | 760 |
| 41 and 17 | 697 |