Least Common Multiple (LCM) of 76 and 108
The least common multiple (LCM) of 76 and 108 is 2052.
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 108?
First, calculate the GCD of 76 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 108 = 0 remainder 76 |
| 2 | 108 ÷ 76 = 1 remainder 32 |
| 3 | 76 ÷ 32 = 2 remainder 12 |
| 4 | 32 ÷ 12 = 2 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 96 | 2208 |
| 12 and 56 | 168 |
| 32 and 110 | 1760 |
| 198 and 22 | 198 |
| 33 and 175 | 5775 |