Least Common Multiple (LCM) of 189 and 55
The least common multiple (LCM) of 189 and 55 is 10395.
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 55?
First, calculate the GCD of 189 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 55 = 3 remainder 24 |
| 2 | 55 ÷ 24 = 2 remainder 7 |
| 3 | 24 ÷ 7 = 3 remainder 3 |
| 4 | 7 ÷ 3 = 2 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 126 | 11844 |
| 42 and 80 | 1680 |
| 80 and 64 | 320 |
| 14 and 131 | 1834 |
| 154 and 116 | 8932 |