Least Common Multiple (LCM) of 137 and 165
The least common multiple (LCM) of 137 and 165 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 137 and 165?
First, calculate the GCD of 137 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 165 = 0 remainder 137 |
| 2 | 165 ÷ 137 = 1 remainder 28 |
| 3 | 137 ÷ 28 = 4 remainder 25 |
| 4 | 28 ÷ 25 = 1 remainder 3 |
| 5 | 25 ÷ 3 = 8 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 12 | 228 |
| 105 and 152 | 15960 |
| 40 and 170 | 680 |
| 26 and 33 | 858 |
| 116 and 63 | 7308 |