Least Common Multiple (LCM) of 125 and 164
The least common multiple (LCM) of 125 and 164 is 20500.
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 164?
First, calculate the GCD of 125 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 164 = 0 remainder 125 |
| 2 | 164 ÷ 125 = 1 remainder 39 |
| 3 | 125 ÷ 39 = 3 remainder 8 |
| 4 | 39 ÷ 8 = 4 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 14 | 1358 |
| 187 and 107 | 20009 |
| 108 and 86 | 4644 |
| 181 and 33 | 5973 |
| 110 and 160 | 1760 |