Least Common Multiple (LCM) of 135 and 164
The least common multiple (LCM) of 135 and 164 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 135 and 164?
First, calculate the GCD of 135 and 164 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 164 = 0 remainder 135 |
| 2 | 164 ÷ 135 = 1 remainder 29 |
| 3 | 135 ÷ 29 = 4 remainder 19 |
| 4 | 29 ÷ 19 = 1 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 133 | 3591 |
| 75 and 196 | 14700 |
| 102 and 84 | 1428 |
| 124 and 74 | 4588 |
| 72 and 128 | 1152 |