Least Common Multiple (LCM) of 109 and 140
The least common multiple (LCM) of 109 and 140 is 15260.
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 109 and 140?
First, calculate the GCD of 109 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 140 = 0 remainder 109 |
| 2 | 140 ÷ 109 = 1 remainder 31 |
| 3 | 109 ÷ 31 = 3 remainder 16 |
| 4 | 31 ÷ 16 = 1 remainder 15 |
| 5 | 16 ÷ 15 = 1 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 93 | 6882 |
| 196 and 120 | 5880 |
| 142 and 135 | 19170 |
| 21 and 68 | 1428 |
| 14 and 169 | 2366 |