Least Common Multiple (LCM) of 111 and 77
The least common multiple (LCM) of 111 and 77 is 8547.
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 77?
First, calculate the GCD of 111 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 77 = 1 remainder 34 |
| 2 | 77 ÷ 34 = 2 remainder 9 |
| 3 | 34 ÷ 9 = 3 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 111 | 15096 |
| 125 and 23 | 2875 |
| 77 and 30 | 2310 |
| 103 and 113 | 11639 |
| 61 and 107 | 6527 |