Least Common Multiple (LCM) of 102 and 119
The least common multiple (LCM) of 102 and 119 is 714.
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 119?
First, calculate the GCD of 102 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 119 = 0 remainder 102 |
| 2 | 119 ÷ 102 = 1 remainder 17 |
| 3 | 102 ÷ 17 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 108 | 14148 |
| 29 and 59 | 1711 |
| 146 and 18 | 1314 |
| 82 and 200 | 8200 |
| 156 and 129 | 6708 |