Least Common Multiple (LCM) of 136 and 165
The least common multiple (LCM) of 136 and 165 is 22440.
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 136 and 165?
First, calculate the GCD of 136 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 165 = 0 remainder 136 |
| 2 | 165 ÷ 136 = 1 remainder 29 |
| 3 | 136 ÷ 29 = 4 remainder 20 |
| 4 | 29 ÷ 20 = 1 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 163 | 18582 |
| 14 and 24 | 168 |
| 144 and 89 | 12816 |
| 103 and 11 | 1133 |
| 177 and 200 | 35400 |