Least Common Multiple (LCM) of 100 and 199
The least common multiple (LCM) of 100 and 199 is 19900.
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 199?
First, calculate the GCD of 100 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 199 = 0 remainder 100 |
| 2 | 199 ÷ 100 = 1 remainder 99 |
| 3 | 100 ÷ 99 = 1 remainder 1 |
| 4 | 99 ÷ 1 = 99 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 15 | 2190 |
| 182 and 71 | 12922 |
| 69 and 62 | 4278 |
| 54 and 108 | 108 |
| 172 and 148 | 6364 |