Least Common Multiple (LCM) of 173 and 189
The least common multiple (LCM) of 173 and 189 is 32697.
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 173 and 189?
First, calculate the GCD of 173 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 189 = 0 remainder 173 |
| 2 | 189 ÷ 173 = 1 remainder 16 |
| 3 | 173 ÷ 16 = 10 remainder 13 |
| 4 | 16 ÷ 13 = 1 remainder 3 |
| 5 | 13 ÷ 3 = 4 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 142 | 7952 |
| 154 and 73 | 11242 |
| 53 and 193 | 10229 |
| 40 and 42 | 840 |
| 16 and 110 | 880 |