Least Common Multiple (LCM) of 102 and 135
The least common multiple (LCM) of 102 and 135 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 102 and 135?
First, calculate the GCD of 102 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 135 = 0 remainder 102 |
| 2 | 135 ÷ 102 = 1 remainder 33 |
| 3 | 102 ÷ 33 = 3 remainder 3 |
| 4 | 33 ÷ 3 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 36 | 5004 |
| 16 and 166 | 1328 |
| 108 and 101 | 10908 |
| 124 and 96 | 2976 |
| 145 and 144 | 20880 |