Least Common Multiple (LCM) of 164 and 135
The least common multiple (LCM) of 164 and 135 is 22140.
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 135?
First, calculate the GCD of 164 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 164 ÷ 135 = 1 remainder 29 |
| 2 | 135 ÷ 29 = 4 remainder 19 |
| 3 | 29 ÷ 19 = 1 remainder 10 |
| 4 | 19 ÷ 10 = 1 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 123 | 17220 |
| 52 and 103 | 5356 |
| 111 and 45 | 1665 |
| 127 and 83 | 10541 |
| 70 and 102 | 3570 |