Least Common Multiple (LCM) of 102 and 140
The least common multiple (LCM) of 102 and 140 is 7140.
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 140?
First, calculate the GCD of 102 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 140 = 0 remainder 102 |
| 2 | 140 ÷ 102 = 1 remainder 38 |
| 3 | 102 ÷ 38 = 2 remainder 26 |
| 4 | 38 ÷ 26 = 1 remainder 12 |
| 5 | 26 ÷ 12 = 2 remainder 2 |
| 6 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 92 and 52 | 1196 |
| 60 and 55 | 660 |
| 10 and 192 | 960 |
| 30 and 69 | 690 |
| 132 and 66 | 132 |