Least Common Multiple (LCM) of 100 and 200
The least common multiple (LCM) of 100 and 200 is 200.
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 200?
First, calculate the GCD of 100 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 200 = 0 remainder 100 |
| 2 | 200 ÷ 100 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 120 | 23160 |
| 109 and 177 | 19293 |
| 75 and 191 | 14325 |
| 36 and 178 | 3204 |
| 148 and 117 | 17316 |