Least Common Multiple (LCM) of 111 and 64
The least common multiple (LCM) of 111 and 64 is 7104.
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 64?
First, calculate the GCD of 111 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 64 = 1 remainder 47 |
| 2 | 64 ÷ 47 = 1 remainder 17 |
| 3 | 47 ÷ 17 = 2 remainder 13 |
| 4 | 17 ÷ 13 = 1 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 169 | 20111 |
| 176 and 97 | 17072 |
| 159 and 191 | 30369 |
| 184 and 103 | 18952 |
| 107 and 67 | 7169 |