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 |
|---|---|
| 116 and 111 | 12876 |
| 120 and 68 | 2040 |
| 87 and 139 | 12093 |
| 100 and 157 | 15700 |
| 99 and 50 | 4950 |