Least Common Multiple (LCM) of 189 and 90
The least common multiple (LCM) of 189 and 90 is 1890.
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 90?
First, calculate the GCD of 189 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 90 = 2 remainder 9 |
| 2 | 90 ÷ 9 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 104 | 3432 |
| 158 and 112 | 8848 |
| 52 and 17 | 884 |
| 139 and 18 | 2502 |
| 40 and 45 | 360 |