Least Common Multiple (LCM) of 189 and 54
The least common multiple (LCM) of 189 and 54 is 378.
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 54?
First, calculate the GCD of 189 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 54 = 3 remainder 27 |
| 2 | 54 ÷ 27 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 112 | 3248 |
| 160 and 68 | 2720 |
| 67 and 123 | 8241 |
| 27 and 143 | 3861 |
| 16 and 150 | 1200 |