Least Common Multiple (LCM) of 102 and 158
The least common multiple (LCM) of 102 and 158 is 8058.
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 158?
First, calculate the GCD of 102 and 158 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 158 = 0 remainder 102 |
| 2 | 158 ÷ 102 = 1 remainder 56 |
| 3 | 102 ÷ 56 = 1 remainder 46 |
| 4 | 56 ÷ 46 = 1 remainder 10 |
| 5 | 46 ÷ 10 = 4 remainder 6 |
| 6 | 10 ÷ 6 = 1 remainder 4 |
| 7 | 6 ÷ 4 = 1 remainder 2 |
| 8 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 156 | 3276 |
| 166 and 63 | 10458 |
| 194 and 106 | 10282 |
| 24 and 82 | 984 |
| 135 and 165 | 1485 |