Least Common Multiple (LCM) of 127 and 170
The least common multiple (LCM) of 127 and 170 is 21590.
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 170?
First, calculate the GCD of 127 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 170 = 0 remainder 127 |
| 2 | 170 ÷ 127 = 1 remainder 43 |
| 3 | 127 ÷ 43 = 2 remainder 41 |
| 4 | 43 ÷ 41 = 1 remainder 2 |
| 5 | 41 ÷ 2 = 20 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 195 | 12285 |
| 112 and 38 | 2128 |
| 21 and 174 | 1218 |
| 16 and 174 | 1392 |
| 62 and 30 | 930 |