Least Common Multiple (LCM) of 125 and 96
The least common multiple (LCM) of 125 and 96 is 12000.
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 96?
First, calculate the GCD of 125 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 96 = 1 remainder 29 |
| 2 | 96 ÷ 29 = 3 remainder 9 |
| 3 | 29 ÷ 9 = 3 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 178 | 9612 |
| 116 and 157 | 18212 |
| 37 and 194 | 7178 |
| 122 and 34 | 2074 |
| 76 and 106 | 4028 |