Least Common Multiple (LCM) of 108 and 165
The least common multiple (LCM) of 108 and 165 is 5940.
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 165?
First, calculate the GCD of 108 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 165 = 0 remainder 108 |
| 2 | 165 ÷ 108 = 1 remainder 57 |
| 3 | 108 ÷ 57 = 1 remainder 51 |
| 4 | 57 ÷ 51 = 1 remainder 6 |
| 5 | 51 ÷ 6 = 8 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 21 | 2856 |
| 128 and 88 | 1408 |
| 114 and 125 | 14250 |
| 29 and 21 | 609 |
| 34 and 66 | 1122 |