Least Common Multiple (LCM) of 172 and 125
The least common multiple (LCM) of 172 and 125 is 21500.
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 125?
First, calculate the GCD of 172 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 125 = 1 remainder 47 |
| 2 | 125 ÷ 47 = 2 remainder 31 |
| 3 | 47 ÷ 31 = 1 remainder 16 |
| 4 | 31 ÷ 16 = 1 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 101 | 9595 |
| 23 and 185 | 4255 |
| 159 and 107 | 17013 |
| 114 and 36 | 684 |
| 105 and 133 | 1995 |