Least Common Multiple (LCM) of 109 and 164
The least common multiple (LCM) of 109 and 164 is 17876.
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 109 and 164?
First, calculate the GCD of 109 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 164 = 0 remainder 109 |
| 2 | 164 ÷ 109 = 1 remainder 55 |
| 3 | 109 ÷ 55 = 1 remainder 54 |
| 4 | 55 ÷ 54 = 1 remainder 1 |
| 5 | 54 ÷ 1 = 54 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 148 | 7844 |
| 182 and 186 | 16926 |
| 168 and 162 | 4536 |
| 20 and 96 | 480 |
| 59 and 89 | 5251 |