Least Common Multiple (LCM) of 168 and 108
The least common multiple (LCM) of 168 and 108 is 1512.
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 168 and 108?
First, calculate the GCD of 168 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 108 = 1 remainder 60 |
| 2 | 108 ÷ 60 = 1 remainder 48 |
| 3 | 60 ÷ 48 = 1 remainder 12 |
| 4 | 48 ÷ 12 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 103 | 18025 |
| 68 and 199 | 13532 |
| 54 and 181 | 9774 |
| 168 and 36 | 504 |
| 13 and 36 | 468 |