Least Common Multiple (LCM) of 125 and 133
The least common multiple (LCM) of 125 and 133 is 16625.
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 133?
First, calculate the GCD of 125 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 133 = 0 remainder 125 |
| 2 | 133 ÷ 125 = 1 remainder 8 |
| 3 | 125 ÷ 8 = 15 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 113 | 3955 |
| 122 and 115 | 14030 |
| 60 and 52 | 780 |
| 168 and 144 | 1008 |
| 135 and 110 | 2970 |