Least Common Multiple (LCM) of 76 and 125
The least common multiple (LCM) of 76 and 125 is 9500.
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 76 and 125?
First, calculate the GCD of 76 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 125 = 0 remainder 76 |
| 2 | 125 ÷ 76 = 1 remainder 49 |
| 3 | 76 ÷ 49 = 1 remainder 27 |
| 4 | 49 ÷ 27 = 1 remainder 22 |
| 5 | 27 ÷ 22 = 1 remainder 5 |
| 6 | 22 ÷ 5 = 4 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 127 | 7747 |
| 25 and 128 | 3200 |
| 49 and 200 | 9800 |
| 140 and 40 | 280 |
| 88 and 176 | 176 |