Least Common Multiple (LCM) of 73 and 189
The least common multiple (LCM) of 73 and 189 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 73 and 189?
First, calculate the GCD of 73 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 189 = 0 remainder 73 |
| 2 | 189 ÷ 73 = 2 remainder 43 |
| 3 | 73 ÷ 43 = 1 remainder 30 |
| 4 | 43 ÷ 30 = 1 remainder 13 |
| 5 | 30 ÷ 13 = 2 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 125 | 8625 |
| 39 and 162 | 2106 |
| 67 and 10 | 670 |
| 20 and 170 | 340 |
| 35 and 51 | 1785 |