Least Common Multiple (LCM) of 32 and 125
The least common multiple (LCM) of 32 and 125 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 32 and 125?
First, calculate the GCD of 32 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 125 = 0 remainder 32 |
| 2 | 125 ÷ 32 = 3 remainder 29 |
| 3 | 32 ÷ 29 = 1 remainder 3 |
| 4 | 29 ÷ 3 = 9 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 197 | 19306 |
| 124 and 16 | 496 |
| 145 and 65 | 1885 |
| 157 and 148 | 23236 |
| 196 and 103 | 20188 |