Least Common Multiple (LCM) of 110 and 139
The least common multiple (LCM) of 110 and 139 is 15290.
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 110 and 139?
First, calculate the GCD of 110 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 139 = 0 remainder 110 |
| 2 | 139 ÷ 110 = 1 remainder 29 |
| 3 | 110 ÷ 29 = 3 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 127 | 12827 |
| 172 and 55 | 9460 |
| 112 and 83 | 9296 |
| 65 and 68 | 4420 |
| 172 and 126 | 10836 |