Least Common Multiple (LCM) of 123 and 162
The least common multiple (LCM) of 123 and 162 is 6642.
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 123 and 162?
First, calculate the GCD of 123 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 162 = 0 remainder 123 |
| 2 | 162 ÷ 123 = 1 remainder 39 |
| 3 | 123 ÷ 39 = 3 remainder 6 |
| 4 | 39 ÷ 6 = 6 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 87 | 9744 |
| 135 and 81 | 405 |
| 51 and 112 | 5712 |
| 126 and 82 | 5166 |
| 132 and 106 | 6996 |