Least Common Multiple (LCM) of 45 and 164
The least common multiple (LCM) of 45 and 164 is 7380.
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 45 and 164?
First, calculate the GCD of 45 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 164 = 0 remainder 45 |
| 2 | 164 ÷ 45 = 3 remainder 29 |
| 3 | 45 ÷ 29 = 1 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 10 | 1090 |
| 132 and 109 | 14388 |
| 193 and 122 | 23546 |
| 111 and 46 | 5106 |
| 38 and 199 | 7562 |