Least Common Multiple (LCM) of 174 and 125
The least common multiple (LCM) of 174 and 125 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 174 and 125?
First, calculate the GCD of 174 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 125 = 1 remainder 49 |
| 2 | 125 ÷ 49 = 2 remainder 27 |
| 3 | 49 ÷ 27 = 1 remainder 22 |
| 4 | 27 ÷ 22 = 1 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 109 | 18748 |
| 47 and 116 | 5452 |
| 32 and 40 | 160 |
| 180 and 154 | 13860 |
| 93 and 68 | 6324 |