Least Common Multiple (LCM) of 100 and 125
The least common multiple (LCM) of 100 and 125 is 500.
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 100 and 125?
First, calculate the GCD of 100 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 125 = 0 remainder 100 |
| 2 | 125 ÷ 100 = 1 remainder 25 |
| 3 | 100 ÷ 25 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 44 | 748 |
| 147 and 35 | 735 |
| 102 and 136 | 408 |
| 30 and 34 | 510 |
| 190 and 199 | 37810 |