Least Common Multiple (LCM) of 105 and 139
The least common multiple (LCM) of 105 and 139 is 14595.
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 105 and 139?
First, calculate the GCD of 105 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 139 = 0 remainder 105 |
| 2 | 139 ÷ 105 = 1 remainder 34 |
| 3 | 105 ÷ 34 = 3 remainder 3 |
| 4 | 34 ÷ 3 = 11 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 188 | 10340 |
| 76 and 139 | 10564 |
| 74 and 87 | 6438 |
| 156 and 190 | 14820 |
| 73 and 157 | 11461 |