Least Common Multiple (LCM) of 127 and 171
The least common multiple (LCM) of 127 and 171 is 21717.
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 171?
First, calculate the GCD of 127 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 171 = 0 remainder 127 |
| 2 | 171 ÷ 127 = 1 remainder 44 |
| 3 | 127 ÷ 44 = 2 remainder 39 |
| 4 | 44 ÷ 39 = 1 remainder 5 |
| 5 | 39 ÷ 5 = 7 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 197 | 38021 |
| 118 and 168 | 9912 |
| 73 and 155 | 11315 |
| 51 and 115 | 5865 |
| 141 and 98 | 13818 |