Least Common Multiple (LCM) of 64 and 69
The least common multiple (LCM) of 64 and 69 is 4416.
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 69?
First, calculate the GCD of 64 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 69 = 0 remainder 64 |
| 2 | 69 ÷ 64 = 1 remainder 5 |
| 3 | 64 ÷ 5 = 12 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 94 | 12502 |
| 180 and 144 | 720 |
| 198 and 160 | 15840 |
| 123 and 11 | 1353 |
| 179 and 21 | 3759 |