Least Common Multiple (LCM) of 165 and 76
The least common multiple (LCM) of 165 and 76 is 12540.
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 76?
First, calculate the GCD of 165 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 76 = 2 remainder 13 |
| 2 | 76 ÷ 13 = 5 remainder 11 |
| 3 | 13 ÷ 11 = 1 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 78 | 78 |
| 89 and 152 | 13528 |
| 43 and 200 | 8600 |
| 169 and 126 | 21294 |
| 52 and 96 | 1248 |