Least Common Multiple (LCM) of 125 and 76
The least common multiple (LCM) of 125 and 76 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 125 and 76?
First, calculate the GCD of 125 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 76 = 1 remainder 49 |
| 2 | 76 ÷ 49 = 1 remainder 27 |
| 3 | 49 ÷ 27 = 1 remainder 22 |
| 4 | 27 ÷ 22 = 1 remainder 5 |
| 5 | 22 ÷ 5 = 4 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 84 and 22 | 924 |
| 25 and 164 | 4100 |
| 99 and 18 | 198 |
| 110 and 111 | 12210 |
| 162 and 116 | 9396 |