Least Common Multiple (LCM) of 108 and 168
The least common multiple (LCM) of 108 and 168 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 108 and 168?
First, calculate the GCD of 108 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 168 = 0 remainder 108 |
| 2 | 168 ÷ 108 = 1 remainder 60 |
| 3 | 108 ÷ 60 = 1 remainder 48 |
| 4 | 60 ÷ 48 = 1 remainder 12 |
| 5 | 48 ÷ 12 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 97 | 18915 |
| 167 and 85 | 14195 |
| 33 and 114 | 1254 |
| 13 and 80 | 1040 |
| 92 and 65 | 5980 |