Least Common Multiple (LCM) of 125 and 102
The least common multiple (LCM) of 125 and 102 is 12750.
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 102?
First, calculate the GCD of 125 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 102 = 1 remainder 23 |
| 2 | 102 ÷ 23 = 4 remainder 10 |
| 3 | 23 ÷ 10 = 2 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 200 | 4200 |
| 37 and 116 | 4292 |
| 105 and 140 | 420 |
| 32 and 70 | 1120 |
| 111 and 128 | 14208 |