Least Common Multiple (LCM) of 64 and 115
The least common multiple (LCM) of 64 and 115 is 7360.
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 115?
First, calculate the GCD of 64 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 115 = 0 remainder 64 |
| 2 | 115 ÷ 64 = 1 remainder 51 |
| 3 | 64 ÷ 51 = 1 remainder 13 |
| 4 | 51 ÷ 13 = 3 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 60 | 2220 |
| 30 and 169 | 5070 |
| 35 and 156 | 5460 |
| 67 and 31 | 2077 |
| 76 and 200 | 3800 |