Least Common Multiple (LCM) of 100 and 195
The least common multiple (LCM) of 100 and 195 is 3900.
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 100 and 195?
First, calculate the GCD of 100 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 195 = 0 remainder 100 |
| 2 | 195 ÷ 100 = 1 remainder 95 |
| 3 | 100 ÷ 95 = 1 remainder 5 |
| 4 | 95 ÷ 5 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 197 | 34475 |
| 102 and 165 | 5610 |
| 59 and 114 | 6726 |
| 167 and 133 | 22211 |
| 190 and 169 | 32110 |