Least Common Multiple (LCM) of 127 and 180
The least common multiple (LCM) of 127 and 180 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 127 and 180?
First, calculate the GCD of 127 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 180 = 0 remainder 127 |
| 2 | 180 ÷ 127 = 1 remainder 53 |
| 3 | 127 ÷ 53 = 2 remainder 21 |
| 4 | 53 ÷ 21 = 2 remainder 11 |
| 5 | 21 ÷ 11 = 1 remainder 10 |
| 6 | 11 ÷ 10 = 1 remainder 1 |
| 7 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 28 | 420 |
| 49 and 119 | 833 |
| 107 and 83 | 8881 |
| 109 and 151 | 16459 |
| 106 and 184 | 9752 |