Least Common Multiple (LCM) of 125 and 33
The least common multiple (LCM) of 125 and 33 is 4125.
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 33?
First, calculate the GCD of 125 and 33 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 33 = 3 remainder 26 |
| 2 | 33 ÷ 26 = 1 remainder 7 |
| 3 | 26 ÷ 7 = 3 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 105 | 1365 |
| 71 and 115 | 8165 |
| 147 and 189 | 1323 |
| 61 and 168 | 10248 |
| 25 and 13 | 325 |