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 |
|---|---|
| 49 and 25 | 1225 |
| 70 and 124 | 4340 |
| 107 and 42 | 4494 |
| 16 and 16 | 16 |
| 163 and 194 | 31622 |