Least Common Multiple (LCM) of 125 and 32
The least common multiple (LCM) of 125 and 32 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 32?
First, calculate the GCD of 125 and 32 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 32 = 3 remainder 29 |
| 2 | 32 ÷ 29 = 1 remainder 3 |
| 3 | 29 ÷ 3 = 9 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 112 | 22288 |
| 74 and 100 | 3700 |
| 199 and 110 | 21890 |
| 141 and 142 | 20022 |
| 17 and 17 | 17 |