Least Common Multiple (LCM) of 125 and 174
The least common multiple (LCM) of 125 and 174 is 21750.
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 174?
First, calculate the GCD of 125 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 174 = 0 remainder 125 |
| 2 | 174 ÷ 125 = 1 remainder 49 |
| 3 | 125 ÷ 49 = 2 remainder 27 |
| 4 | 49 ÷ 27 = 1 remainder 22 |
| 5 | 27 ÷ 22 = 1 remainder 5 |
| 6 | 22 ÷ 5 = 4 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 143 | 6578 |
| 32 and 78 | 1248 |
| 195 and 198 | 12870 |
| 191 and 68 | 12988 |
| 145 and 127 | 18415 |