Least Common Multiple (LCM) of 111 and 168
The least common multiple (LCM) of 111 and 168 is 6216.
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 111 and 168?
First, calculate the GCD of 111 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 168 = 0 remainder 111 |
| 2 | 168 ÷ 111 = 1 remainder 57 |
| 3 | 111 ÷ 57 = 1 remainder 54 |
| 4 | 57 ÷ 54 = 1 remainder 3 |
| 5 | 54 ÷ 3 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 39 | 6123 |
| 102 and 78 | 1326 |
| 36 and 41 | 1476 |
| 56 and 48 | 336 |
| 137 and 106 | 14522 |