Least Common Multiple (LCM) of 91 and 125
The least common multiple (LCM) of 91 and 125 is 11375.
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 91 and 125?
First, calculate the GCD of 91 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 125 = 0 remainder 91 |
| 2 | 125 ÷ 91 = 1 remainder 34 |
| 3 | 91 ÷ 34 = 2 remainder 23 |
| 4 | 34 ÷ 23 = 1 remainder 11 |
| 5 | 23 ÷ 11 = 2 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 90 | 1170 |
| 188 and 128 | 6016 |
| 14 and 39 | 546 |
| 44 and 147 | 6468 |
| 71 and 120 | 8520 |