Least Common Multiple (LCM) of 108 and 76
The least common multiple (LCM) of 108 and 76 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 108 and 76?
First, calculate the GCD of 108 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 76 = 1 remainder 32 |
| 2 | 76 ÷ 32 = 2 remainder 12 |
| 3 | 32 ÷ 12 = 2 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 133 | 2394 |
| 123 and 177 | 7257 |
| 55 and 17 | 935 |
| 185 and 120 | 4440 |
| 115 and 61 | 7015 |