Least Common Multiple (LCM) of 114 and 102
The least common multiple (LCM) of 114 and 102 is 1938.
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 114 and 102?
First, calculate the GCD of 114 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 102 = 1 remainder 12 |
| 2 | 102 ÷ 12 = 8 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 155 | 2790 |
| 107 and 113 | 12091 |
| 80 and 51 | 4080 |
| 155 and 186 | 930 |
| 154 and 98 | 1078 |