Least Common Multiple (LCM) of 102 and 162
The least common multiple (LCM) of 102 and 162 is 2754.
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 162?
First, calculate the GCD of 102 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 162 = 0 remainder 102 |
| 2 | 162 ÷ 102 = 1 remainder 60 |
| 3 | 102 ÷ 60 = 1 remainder 42 |
| 4 | 60 ÷ 42 = 1 remainder 18 |
| 5 | 42 ÷ 18 = 2 remainder 6 |
| 6 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 90 | 6390 |
| 38 and 102 | 1938 |
| 165 and 84 | 4620 |
| 178 and 136 | 12104 |
| 125 and 18 | 2250 |