Least Common Multiple (LCM) of 164 and 105
The least common multiple (LCM) of 164 and 105 is 17220.
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 105?
First, calculate the GCD of 164 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 105 = 1 remainder 59 |
| 2 | 105 ÷ 59 = 1 remainder 46 |
| 3 | 59 ÷ 46 = 1 remainder 13 |
| 4 | 46 ÷ 13 = 3 remainder 7 |
| 5 | 13 ÷ 7 = 1 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 128 | 9856 |
| 36 and 183 | 2196 |
| 195 and 117 | 585 |
| 141 and 178 | 25098 |
| 180 and 32 | 1440 |