Least Common Multiple (LCM) of 76 and 165
The least common multiple (LCM) of 76 and 165 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 76 and 165?
First, calculate the GCD of 76 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 165 = 0 remainder 76 |
| 2 | 165 ÷ 76 = 2 remainder 13 |
| 3 | 76 ÷ 13 = 5 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 146 | 10512 |
| 124 and 77 | 9548 |
| 120 and 108 | 1080 |
| 24 and 24 | 24 |
| 50 and 155 | 1550 |