Least Common Multiple (LCM) of 127 and 165
The least common multiple (LCM) of 127 and 165 is 20955.
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 127 and 165?
First, calculate the GCD of 127 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 165 = 0 remainder 127 |
| 2 | 165 ÷ 127 = 1 remainder 38 |
| 3 | 127 ÷ 38 = 3 remainder 13 |
| 4 | 38 ÷ 13 = 2 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 39 | 585 |
| 193 and 187 | 36091 |
| 140 and 175 | 700 |
| 117 and 106 | 12402 |
| 81 and 107 | 8667 |