Least Common Multiple (LCM) of 162 and 102
The least common multiple (LCM) of 162 and 102 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 162 and 102?
First, calculate the GCD of 162 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 102 = 1 remainder 60 |
| 2 | 102 ÷ 60 = 1 remainder 42 |
| 3 | 60 ÷ 42 = 1 remainder 18 |
| 4 | 42 ÷ 18 = 2 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 79 | 10191 |
| 193 and 199 | 38407 |
| 114 and 167 | 19038 |
| 145 and 114 | 16530 |
| 21 and 142 | 2982 |