Least Common Multiple (LCM) of 33 and 125
The least common multiple (LCM) of 33 and 125 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 33 and 125?
First, calculate the GCD of 33 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 33 ÷ 125 = 0 remainder 33 |
| 2 | 125 ÷ 33 = 3 remainder 26 |
| 3 | 33 ÷ 26 = 1 remainder 7 |
| 4 | 26 ÷ 7 = 3 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 84 | 336 |
| 46 and 20 | 460 |
| 167 and 40 | 6680 |
| 186 and 17 | 3162 |
| 189 and 156 | 9828 |