Least Common Multiple (LCM) of 164 and 106
The least common multiple (LCM) of 164 and 106 is 8692.
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 106?
First, calculate the GCD of 164 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 106 = 1 remainder 58 |
| 2 | 106 ÷ 58 = 1 remainder 48 |
| 3 | 58 ÷ 48 = 1 remainder 10 |
| 4 | 48 ÷ 10 = 4 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 137 | 16851 |
| 24 and 114 | 456 |
| 144 and 97 | 13968 |
| 162 and 176 | 14256 |
| 14 and 85 | 1190 |