Least Common Multiple (LCM) of 189 and 99
The least common multiple (LCM) of 189 and 99 is 2079.
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 189 and 99?
First, calculate the GCD of 189 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 99 = 1 remainder 90 |
| 2 | 99 ÷ 90 = 1 remainder 9 |
| 3 | 90 ÷ 9 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 189 | 1890 |
| 169 and 68 | 11492 |
| 101 and 155 | 15655 |
| 28 and 195 | 5460 |
| 37 and 70 | 2590 |