Least Common Multiple (LCM) of 96 and 164
The least common multiple (LCM) of 96 and 164 is 3936.
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 164?
First, calculate the GCD of 96 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 164 = 0 remainder 96 |
| 2 | 164 ÷ 96 = 1 remainder 68 |
| 3 | 96 ÷ 68 = 1 remainder 28 |
| 4 | 68 ÷ 28 = 2 remainder 12 |
| 5 | 28 ÷ 12 = 2 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 179 | 7697 |
| 190 and 43 | 8170 |
| 87 and 146 | 12702 |
| 45 and 115 | 1035 |
| 20 and 72 | 360 |