Least Common Multiple (LCM) of 75 and 125
The least common multiple (LCM) of 75 and 125 is 375.
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 75 and 125?
First, calculate the GCD of 75 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 125 = 0 remainder 75 |
| 2 | 125 ÷ 75 = 1 remainder 50 |
| 3 | 75 ÷ 50 = 1 remainder 25 |
| 4 | 50 ÷ 25 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 83 | 15521 |
| 179 and 145 | 25955 |
| 13 and 97 | 1261 |
| 120 and 173 | 20760 |
| 156 and 118 | 9204 |