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 |
|---|---|
| 73 and 115 | 8395 |
| 179 and 103 | 18437 |
| 61 and 100 | 6100 |
| 118 and 109 | 12862 |
| 181 and 87 | 15747 |