Least Common Multiple (LCM) of 102 and 139
The least common multiple (LCM) of 102 and 139 is 14178.
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 102 and 139?
First, calculate the GCD of 102 and 139 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 139 = 0 remainder 102 |
| 2 | 139 ÷ 102 = 1 remainder 37 |
| 3 | 102 ÷ 37 = 2 remainder 28 |
| 4 | 37 ÷ 28 = 1 remainder 9 |
| 5 | 28 ÷ 9 = 3 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 106 | 11342 |
| 23 and 87 | 2001 |
| 162 and 54 | 162 |
| 101 and 13 | 1313 |
| 23 and 163 | 3749 |