Least Common Multiple (LCM) of 96 and 122
The least common multiple (LCM) of 96 and 122 is 5856.
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 96 and 122?
First, calculate the GCD of 96 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 122 = 0 remainder 96 |
| 2 | 122 ÷ 96 = 1 remainder 26 |
| 3 | 96 ÷ 26 = 3 remainder 18 |
| 4 | 26 ÷ 18 = 1 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 39 | 6864 |
| 40 and 13 | 520 |
| 126 and 85 | 10710 |
| 14 and 108 | 756 |
| 147 and 192 | 9408 |