Least Common Multiple (LCM) of 125 and 78
The least common multiple (LCM) of 125 and 78 is 9750.
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 78?
First, calculate the GCD of 125 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 78 = 1 remainder 47 |
| 2 | 78 ÷ 47 = 1 remainder 31 |
| 3 | 47 ÷ 31 = 1 remainder 16 |
| 4 | 31 ÷ 16 = 1 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 76 | 3420 |
| 145 and 105 | 3045 |
| 142 and 153 | 21726 |
| 24 and 198 | 792 |
| 27 and 187 | 5049 |