Least Common Multiple (LCM) of 64 and 111
The least common multiple (LCM) of 64 and 111 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 64 and 111?
First, calculate the GCD of 64 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 111 = 0 remainder 64 |
| 2 | 111 ÷ 64 = 1 remainder 47 |
| 3 | 64 ÷ 47 = 1 remainder 17 |
| 4 | 47 ÷ 17 = 2 remainder 13 |
| 5 | 17 ÷ 13 = 1 remainder 4 |
| 6 | 13 ÷ 4 = 3 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 46 | 1794 |
| 30 and 138 | 690 |
| 130 and 176 | 11440 |
| 68 and 14 | 476 |
| 112 and 22 | 1232 |