Least Common Multiple (LCM) of 69 and 165
The least common multiple (LCM) of 69 and 165 is 3795.
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 69 and 165?
First, calculate the GCD of 69 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 165 = 0 remainder 69 |
| 2 | 165 ÷ 69 = 2 remainder 27 |
| 3 | 69 ÷ 27 = 2 remainder 15 |
| 4 | 27 ÷ 15 = 1 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 180 | 4140 |
| 95 and 164 | 15580 |
| 131 and 161 | 21091 |
| 17 and 13 | 221 |
| 71 and 144 | 10224 |