Least Common Multiple (LCM) of 127 and 178
The least common multiple (LCM) of 127 and 178 is 22606.
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 178?
First, calculate the GCD of 127 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 178 = 0 remainder 127 |
| 2 | 178 ÷ 127 = 1 remainder 51 |
| 3 | 127 ÷ 51 = 2 remainder 25 |
| 4 | 51 ÷ 25 = 2 remainder 1 |
| 5 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 195 | 1755 |
| 13 and 81 | 1053 |
| 98 and 180 | 8820 |
| 125 and 41 | 5125 |
| 101 and 30 | 3030 |