Least Common Multiple (LCM) of 125 and 172
The least common multiple (LCM) of 125 and 172 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 125 and 172?
First, calculate the GCD of 125 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 172 = 0 remainder 125 |
| 2 | 172 ÷ 125 = 1 remainder 47 |
| 3 | 125 ÷ 47 = 2 remainder 31 |
| 4 | 47 ÷ 31 = 1 remainder 16 |
| 5 | 31 ÷ 16 = 1 remainder 15 |
| 6 | 16 ÷ 15 = 1 remainder 1 |
| 7 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 102 | 3570 |
| 32 and 172 | 1376 |
| 154 and 165 | 2310 |
| 48 and 57 | 912 |
| 200 and 146 | 14600 |