Least Common Multiple (LCM) of 114 and 64
The least common multiple (LCM) of 114 and 64 is 3648.
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 114 and 64?
First, calculate the GCD of 114 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 64 = 1 remainder 50 |
| 2 | 64 ÷ 50 = 1 remainder 14 |
| 3 | 50 ÷ 14 = 3 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 82 | 2132 |
| 155 and 54 | 8370 |
| 196 and 75 | 14700 |
| 183 and 104 | 19032 |
| 97 and 181 | 17557 |