Least Common Multiple (LCM) of 105 and 164
The least common multiple (LCM) of 105 and 164 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 105 and 164?
First, calculate the GCD of 105 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 164 = 0 remainder 105 |
| 2 | 164 ÷ 105 = 1 remainder 59 |
| 3 | 105 ÷ 59 = 1 remainder 46 |
| 4 | 59 ÷ 46 = 1 remainder 13 |
| 5 | 46 ÷ 13 = 3 remainder 7 |
| 6 | 13 ÷ 7 = 1 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 112 | 1232 |
| 158 and 102 | 8058 |
| 48 and 190 | 4560 |
| 133 and 170 | 22610 |
| 103 and 118 | 12154 |