Least Common Multiple (LCM) of 99 and 188
The least common multiple (LCM) of 99 and 188 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 99 and 188?
First, calculate the GCD of 99 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 188 = 0 remainder 99 |
| 2 | 188 ÷ 99 = 1 remainder 89 |
| 3 | 99 ÷ 89 = 1 remainder 10 |
| 4 | 89 ÷ 10 = 8 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 172 | 6708 |
| 102 and 154 | 7854 |
| 147 and 12 | 588 |
| 182 and 132 | 12012 |
| 200 and 12 | 600 |