Least Common Multiple (LCM) of 189 and 73
The least common multiple (LCM) of 189 and 73 is 13797.
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 73?
First, calculate the GCD of 189 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 73 = 2 remainder 43 |
| 2 | 73 ÷ 43 = 1 remainder 30 |
| 3 | 43 ÷ 30 = 1 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 122 | 18910 |
| 159 and 32 | 5088 |
| 21 and 13 | 273 |
| 30 and 96 | 480 |
| 43 and 135 | 5805 |