Least Common Multiple (LCM) of 111 and 76
The least common multiple (LCM) of 111 and 76 is 8436.
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 111 and 76?
First, calculate the GCD of 111 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 76 = 1 remainder 35 |
| 2 | 76 ÷ 35 = 2 remainder 6 |
| 3 | 35 ÷ 6 = 5 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 104 | 728 |
| 138 and 188 | 12972 |
| 96 and 41 | 3936 |
| 71 and 163 | 11573 |
| 135 and 61 | 8235 |