Least Common Multiple (LCM) of 108 and 164
The least common multiple (LCM) of 108 and 164 is 4428.
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 108 and 164?
First, calculate the GCD of 108 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 164 = 0 remainder 108 |
| 2 | 164 ÷ 108 = 1 remainder 56 |
| 3 | 108 ÷ 56 = 1 remainder 52 |
| 4 | 56 ÷ 52 = 1 remainder 4 |
| 5 | 52 ÷ 4 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 132 | 132 |
| 35 and 12 | 420 |
| 100 and 100 | 100 |
| 119 and 75 | 8925 |
| 92 and 79 | 7268 |