Least Common Multiple (LCM) of 125 and 176
The least common multiple (LCM) of 125 and 176 is 22000.
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 176?
First, calculate the GCD of 125 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 176 = 0 remainder 125 |
| 2 | 176 ÷ 125 = 1 remainder 51 |
| 3 | 125 ÷ 51 = 2 remainder 23 |
| 4 | 51 ÷ 23 = 2 remainder 5 |
| 5 | 23 ÷ 5 = 4 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 |
|---|---|
| 147 and 198 | 9702 |
| 38 and 83 | 3154 |
| 198 and 149 | 29502 |
| 178 and 135 | 24030 |
| 181 and 187 | 33847 |