Least Common Multiple (LCM) of 195 and 116
The least common multiple (LCM) of 195 and 116 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 195 and 116?
First, calculate the GCD of 195 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 116 = 1 remainder 79 |
| 2 | 116 ÷ 79 = 1 remainder 37 |
| 3 | 79 ÷ 37 = 2 remainder 5 |
| 4 | 37 ÷ 5 = 7 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 120 | 1320 |
| 195 and 178 | 34710 |
| 76 and 178 | 6764 |
| 58 and 104 | 3016 |
| 128 and 156 | 4992 |