Least Common Multiple (LCM) of 109 and 165
The least common multiple (LCM) of 109 and 165 is 17985.
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 109 and 165?
First, calculate the GCD of 109 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 165 = 0 remainder 109 |
| 2 | 165 ÷ 109 = 1 remainder 56 |
| 3 | 109 ÷ 56 = 1 remainder 53 |
| 4 | 56 ÷ 53 = 1 remainder 3 |
| 5 | 53 ÷ 3 = 17 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 28 | 420 |
| 160 and 30 | 480 |
| 129 and 169 | 21801 |
| 28 and 111 | 3108 |
| 32 and 40 | 160 |