Least Common Multiple (LCM) of 99 and 190
The least common multiple (LCM) of 99 and 190 is 18810.
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 190?
First, calculate the GCD of 99 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 190 = 0 remainder 99 |
| 2 | 190 ÷ 99 = 1 remainder 91 |
| 3 | 99 ÷ 91 = 1 remainder 8 |
| 4 | 91 ÷ 8 = 11 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 55 | 8360 |
| 131 and 60 | 7860 |
| 144 and 150 | 3600 |
| 111 and 164 | 18204 |
| 88 and 114 | 5016 |