Least Common Multiple (LCM) of 23 and 64
The least common multiple (LCM) of 23 and 64 is 1472.
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 23 and 64?
First, calculate the GCD of 23 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 64 = 0 remainder 23 |
| 2 | 64 ÷ 23 = 2 remainder 18 |
| 3 | 23 ÷ 18 = 1 remainder 5 |
| 4 | 18 ÷ 5 = 3 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 109 | 14715 |
| 96 and 78 | 1248 |
| 164 and 97 | 15908 |
| 119 and 128 | 15232 |
| 108 and 72 | 216 |