Least Common Multiple (LCM) of 135 and 102
The least common multiple (LCM) of 135 and 102 is 4590.
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 102?
First, calculate the GCD of 135 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 102 = 1 remainder 33 |
| 2 | 102 ÷ 33 = 3 remainder 3 |
| 3 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 164 | 7052 |
| 65 and 15 | 195 |
| 148 and 109 | 16132 |
| 94 and 140 | 6580 |
| 54 and 78 | 702 |