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 |
|---|---|
| 199 and 51 | 10149 |
| 154 and 10 | 770 |
| 170 and 199 | 33830 |
| 168 and 23 | 3864 |
| 85 and 173 | 14705 |