Least Common Multiple (LCM) of 138 and 165
The least common multiple (LCM) of 138 and 165 is 7590.
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 138 and 165?
First, calculate the GCD of 138 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 165 = 0 remainder 138 |
| 2 | 165 ÷ 138 = 1 remainder 27 |
| 3 | 138 ÷ 27 = 5 remainder 3 |
| 4 | 27 ÷ 3 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 59 | 6844 |
| 161 and 147 | 3381 |
| 109 and 136 | 14824 |
| 20 and 178 | 1780 |
| 155 and 188 | 29140 |