Least Common Multiple (LCM) of 187 and 100
The least common multiple (LCM) of 187 and 100 is 18700.
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 187 and 100?
First, calculate the GCD of 187 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 100 = 1 remainder 87 |
| 2 | 100 ÷ 87 = 1 remainder 13 |
| 3 | 87 ÷ 13 = 6 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 130 | 390 |
| 198 and 186 | 6138 |
| 60 and 75 | 300 |
| 168 and 121 | 20328 |
| 174 and 55 | 9570 |