Least Common Multiple (LCM) of 125 and 84
The least common multiple (LCM) of 125 and 84 is 10500.
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 84?
First, calculate the GCD of 125 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 84 = 1 remainder 41 |
| 2 | 84 ÷ 41 = 2 remainder 2 |
| 3 | 41 ÷ 2 = 20 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 124 | 3100 |
| 122 and 19 | 2318 |
| 160 and 147 | 23520 |
| 18 and 117 | 234 |
| 38 and 18 | 342 |