Least Common Multiple (LCM) of 164 and 115
The least common multiple (LCM) of 164 and 115 is 18860.
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 115?
First, calculate the GCD of 164 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 115 = 1 remainder 49 |
| 2 | 115 ÷ 49 = 2 remainder 17 |
| 3 | 49 ÷ 17 = 2 remainder 15 |
| 4 | 17 ÷ 15 = 1 remainder 2 |
| 5 | 15 ÷ 2 = 7 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 86 | 2666 |
| 160 and 127 | 20320 |
| 51 and 149 | 7599 |
| 27 and 182 | 4914 |
| 50 and 100 | 100 |