Least Common Multiple (LCM) of 172 and 127
The least common multiple (LCM) of 172 and 127 is 21844.
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 172 and 127?
First, calculate the GCD of 172 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 127 = 1 remainder 45 |
| 2 | 127 ÷ 45 = 2 remainder 37 |
| 3 | 45 ÷ 37 = 1 remainder 8 |
| 4 | 37 ÷ 8 = 4 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 117 | 20124 |
| 96 and 173 | 16608 |
| 173 and 87 | 15051 |
| 144 and 177 | 8496 |
| 67 and 15 | 1005 |