Least Common Multiple (LCM) of 165 and 137
The least common multiple (LCM) of 165 and 137 is 22605.
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 165 and 137?
First, calculate the GCD of 165 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 137 = 1 remainder 28 |
| 2 | 137 ÷ 28 = 4 remainder 25 |
| 3 | 28 ÷ 25 = 1 remainder 3 |
| 4 | 25 ÷ 3 = 8 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 59 | 1770 |
| 69 and 74 | 5106 |
| 85 and 159 | 13515 |
| 138 and 124 | 8556 |
| 50 and 132 | 3300 |