Least Common Multiple (LCM) of 102 and 118
The least common multiple (LCM) of 102 and 118 is 6018.
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 118?
First, calculate the GCD of 102 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 118 = 0 remainder 102 |
| 2 | 118 ÷ 102 = 1 remainder 16 |
| 3 | 102 ÷ 16 = 6 remainder 6 |
| 4 | 16 ÷ 6 = 2 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 14 | 2618 |
| 29 and 27 | 783 |
| 67 and 54 | 3618 |
| 142 and 43 | 6106 |
| 162 and 131 | 21222 |