Least Common Multiple (LCM) of 71 and 125
The least common multiple (LCM) of 71 and 125 is 8875.
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 71 and 125?
First, calculate the GCD of 71 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 125 = 0 remainder 71 |
| 2 | 125 ÷ 71 = 1 remainder 54 |
| 3 | 71 ÷ 54 = 1 remainder 17 |
| 4 | 54 ÷ 17 = 3 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 13 | 1157 |
| 28 and 88 | 616 |
| 100 and 137 | 13700 |
| 134 and 200 | 13400 |
| 108 and 27 | 108 |