Least Common Multiple (LCM) of 164 and 96
The least common multiple (LCM) of 164 and 96 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 164 and 96?
First, calculate the GCD of 164 and 96 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 96 = 1 remainder 68 |
| 2 | 96 ÷ 68 = 1 remainder 28 |
| 3 | 68 ÷ 28 = 2 remainder 12 |
| 4 | 28 ÷ 12 = 2 remainder 4 |
| 5 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 110 | 3410 |
| 146 and 144 | 10512 |
| 69 and 100 | 6900 |
| 17 and 152 | 2584 |
| 69 and 102 | 2346 |