Least Common Multiple (LCM) of 178 and 125
The least common multiple (LCM) of 178 and 125 is 22250.
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 178 and 125?
First, calculate the GCD of 178 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 125 = 1 remainder 53 |
| 2 | 125 ÷ 53 = 2 remainder 19 |
| 3 | 53 ÷ 19 = 2 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 23 | 1633 |
| 71 and 138 | 9798 |
| 15 and 25 | 75 |
| 153 and 190 | 29070 |
| 187 and 31 | 5797 |