Least Common Multiple (LCM) of 76 and 111
The least common multiple (LCM) of 76 and 111 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 76 and 111?
First, calculate the GCD of 76 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 111 = 0 remainder 76 |
| 2 | 111 ÷ 76 = 1 remainder 35 |
| 3 | 76 ÷ 35 = 2 remainder 6 |
| 4 | 35 ÷ 6 = 5 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 78 | 10374 |
| 78 and 44 | 1716 |
| 10 and 34 | 170 |
| 177 and 121 | 21417 |
| 60 and 19 | 1140 |