Least Common Multiple (LCM) of 84 and 139
The least common multiple (LCM) of 84 and 139 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 84 and 139?
First, calculate the GCD of 84 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 139 = 0 remainder 84 |
| 2 | 139 ÷ 84 = 1 remainder 55 |
| 3 | 84 ÷ 55 = 1 remainder 29 |
| 4 | 55 ÷ 29 = 1 remainder 26 |
| 5 | 29 ÷ 26 = 1 remainder 3 |
| 6 | 26 ÷ 3 = 8 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 126 | 8946 |
| 46 and 126 | 2898 |
| 11 and 123 | 1353 |
| 21 and 108 | 756 |
| 84 and 46 | 1932 |