Least Common Multiple (LCM) of 111 and 165
The least common multiple (LCM) of 111 and 165 is 6105.
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 165?
First, calculate the GCD of 111 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 165 = 0 remainder 111 |
| 2 | 165 ÷ 111 = 1 remainder 54 |
| 3 | 111 ÷ 54 = 2 remainder 3 |
| 4 | 54 ÷ 3 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 187 | 10098 |
| 140 and 195 | 5460 |
| 98 and 192 | 9408 |
| 41 and 100 | 4100 |
| 123 and 65 | 7995 |