Least Common Multiple (LCM) of 187 and 200
The least common multiple (LCM) of 187 and 200 is 37400.
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 200?
First, calculate the GCD of 187 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 200 = 0 remainder 187 |
| 2 | 200 ÷ 187 = 1 remainder 13 |
| 3 | 187 ÷ 13 = 14 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 102 | 5610 |
| 167 and 61 | 10187 |
| 78 and 107 | 8346 |
| 38 and 124 | 2356 |
| 20 and 174 | 1740 |