Least Common Multiple (LCM) of 125 and 160
The least common multiple (LCM) of 125 and 160 is 4000.
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 160?
First, calculate the GCD of 125 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 160 = 0 remainder 125 |
| 2 | 160 ÷ 125 = 1 remainder 35 |
| 3 | 125 ÷ 35 = 3 remainder 20 |
| 4 | 35 ÷ 20 = 1 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 110 | 110 |
| 186 and 20 | 1860 |
| 153 and 56 | 8568 |
| 85 and 57 | 4845 |
| 49 and 57 | 2793 |