Least Common Multiple (LCM) of 102 and 190
The least common multiple (LCM) of 102 and 190 is 9690.
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 190?
First, calculate the GCD of 102 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 190 = 0 remainder 102 |
| 2 | 190 ÷ 102 = 1 remainder 88 |
| 3 | 102 ÷ 88 = 1 remainder 14 |
| 4 | 88 ÷ 14 = 6 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 109 | 17440 |
| 175 and 111 | 19425 |
| 154 and 160 | 12320 |
| 78 and 173 | 13494 |
| 22 and 143 | 286 |