Least Common Multiple (LCM) of 108 and 125
The least common multiple (LCM) of 108 and 125 is 13500.
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 108 and 125?
First, calculate the GCD of 108 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 125 = 0 remainder 108 |
| 2 | 125 ÷ 108 = 1 remainder 17 |
| 3 | 108 ÷ 17 = 6 remainder 6 |
| 4 | 17 ÷ 6 = 2 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 163 | 23798 |
| 125 and 138 | 17250 |
| 17 and 65 | 1105 |
| 139 and 121 | 16819 |
| 42 and 45 | 630 |