Least Common Multiple (LCM) of 108 and 162
The least common multiple (LCM) of 108 and 162 is 324.
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 108 and 162?
First, calculate the GCD of 108 and 162 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 162 = 0 remainder 108 |
| 2 | 162 ÷ 108 = 1 remainder 54 |
| 3 | 108 ÷ 54 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 40 | 120 |
| 46 and 69 | 138 |
| 120 and 112 | 1680 |
| 157 and 17 | 2669 |
| 21 and 196 | 588 |