Least Common Multiple (LCM) of 127 and 189
The least common multiple (LCM) of 127 and 189 is 24003.
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 127 and 189?
First, calculate the GCD of 127 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 189 = 0 remainder 127 |
| 2 | 189 ÷ 127 = 1 remainder 62 |
| 3 | 127 ÷ 62 = 2 remainder 3 |
| 4 | 62 ÷ 3 = 20 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 80 | 1840 |
| 187 and 66 | 1122 |
| 47 and 110 | 5170 |
| 95 and 11 | 1045 |
| 12 and 56 | 168 |