Least Common Multiple (LCM) of 139 and 84
The least common multiple (LCM) of 139 and 84 is 11676.
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 139 and 84?
First, calculate the GCD of 139 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 139 ÷ 84 = 1 remainder 55 |
| 2 | 84 ÷ 55 = 1 remainder 29 |
| 3 | 55 ÷ 29 = 1 remainder 26 |
| 4 | 29 ÷ 26 = 1 remainder 3 |
| 5 | 26 ÷ 3 = 8 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 110 | 1430 |
| 85 and 40 | 680 |
| 112 and 39 | 4368 |
| 121 and 142 | 17182 |
| 89 and 179 | 15931 |