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 |
|---|---|
| 32 and 188 | 1504 |
| 99 and 157 | 15543 |
| 113 and 14 | 1582 |
| 43 and 47 | 2021 |
| 74 and 106 | 3922 |