Least Common Multiple (LCM) of 180 and 127
The least common multiple (LCM) of 180 and 127 is 22860.
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 180 and 127?
First, calculate the GCD of 180 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 127 = 1 remainder 53 |
| 2 | 127 ÷ 53 = 2 remainder 21 |
| 3 | 53 ÷ 21 = 2 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 111 | 5106 |
| 20 and 102 | 1020 |
| 188 and 93 | 17484 |
| 38 and 99 | 3762 |
| 21 and 173 | 3633 |