Least Common Multiple (LCM) of 125 and 117
The least common multiple (LCM) of 125 and 117 is 14625.
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 117?
First, calculate the GCD of 125 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 117 = 1 remainder 8 |
| 2 | 117 ÷ 8 = 14 remainder 5 |
| 3 | 8 ÷ 5 = 1 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 39 | 4251 |
| 33 and 16 | 528 |
| 176 and 81 | 14256 |
| 145 and 145 | 145 |
| 17 and 93 | 1581 |