Least Common Multiple (LCM) of 67 and 64
The least common multiple (LCM) of 67 and 64 is 4288.
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 67 and 64?
First, calculate the GCD of 67 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 64 = 1 remainder 3 |
| 2 | 64 ÷ 3 = 21 remainder 1 |
| 3 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 69 | 2553 |
| 17 and 185 | 3145 |
| 43 and 123 | 5289 |
| 124 and 85 | 10540 |
| 144 and 36 | 144 |