Least Common Multiple (LCM) of 125 and 168
The least common multiple (LCM) of 125 and 168 is 21000.
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 168?
First, calculate the GCD of 125 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 168 = 0 remainder 125 |
| 2 | 168 ÷ 125 = 1 remainder 43 |
| 3 | 125 ÷ 43 = 2 remainder 39 |
| 4 | 43 ÷ 39 = 1 remainder 4 |
| 5 | 39 ÷ 4 = 9 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 160 | 18720 |
| 73 and 189 | 13797 |
| 41 and 92 | 3772 |
| 47 and 46 | 2162 |
| 185 and 121 | 22385 |