Least Common Multiple (LCM) of 188 and 99
The least common multiple (LCM) of 188 and 99 is 18612.
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 188 and 99?
First, calculate the GCD of 188 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 99 = 1 remainder 89 |
| 2 | 99 ÷ 89 = 1 remainder 10 |
| 3 | 89 ÷ 10 = 8 remainder 9 |
| 4 | 10 ÷ 9 = 1 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 38 | 3534 |
| 129 and 31 | 3999 |
| 181 and 183 | 33123 |
| 110 and 197 | 21670 |
| 11 and 143 | 143 |