Least Common Multiple (LCM) of 100 and 190
The least common multiple (LCM) of 100 and 190 is 1900.
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 190?
First, calculate the GCD of 100 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 190 = 0 remainder 100 |
| 2 | 190 ÷ 100 = 1 remainder 90 |
| 3 | 100 ÷ 90 = 1 remainder 10 |
| 4 | 90 ÷ 10 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 34 | 646 |
| 20 and 77 | 1540 |
| 25 and 129 | 3225 |
| 12 and 21 | 84 |
| 45 and 15 | 45 |