Least Common Multiple (LCM) of 164 and 145
The least common multiple (LCM) of 164 and 145 is 23780.
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 145?
First, calculate the GCD of 164 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 145 = 1 remainder 19 |
| 2 | 145 ÷ 19 = 7 remainder 12 |
| 3 | 19 ÷ 12 = 1 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 134 | 14070 |
| 16 and 76 | 304 |
| 58 and 49 | 2842 |
| 160 and 72 | 1440 |
| 155 and 103 | 15965 |