Least Common Multiple (LCM) of 109 and 139
The least common multiple (LCM) of 109 and 139 is 15151.
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 139?
First, calculate the GCD of 109 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 139 = 0 remainder 109 |
| 2 | 139 ÷ 109 = 1 remainder 30 |
| 3 | 109 ÷ 30 = 3 remainder 19 |
| 4 | 30 ÷ 19 = 1 remainder 11 |
| 5 | 19 ÷ 11 = 1 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 128 | 2688 |
| 156 and 125 | 19500 |
| 76 and 163 | 12388 |
| 90 and 194 | 8730 |
| 200 and 130 | 2600 |