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 |
|---|---|
| 114 and 36 | 684 |
| 137 and 99 | 13563 |
| 47 and 88 | 4136 |
| 10 and 153 | 1530 |
| 31 and 23 | 713 |