Least Common Multiple (LCM) of 107 and 164
The least common multiple (LCM) of 107 and 164 is 17548.
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 107 and 164?
First, calculate the GCD of 107 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 164 = 0 remainder 107 |
| 2 | 164 ÷ 107 = 1 remainder 57 |
| 3 | 107 ÷ 57 = 1 remainder 50 |
| 4 | 57 ÷ 50 = 1 remainder 7 |
| 5 | 50 ÷ 7 = 7 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 109 | 6431 |
| 137 and 65 | 8905 |
| 177 and 186 | 10974 |
| 180 and 134 | 12060 |
| 123 and 148 | 18204 |