Least Common Multiple (LCM) of 64 and 103
The least common multiple (LCM) of 64 and 103 is 6592.
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 103?
First, calculate the GCD of 64 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 64 ÷ 103 = 0 remainder 64 |
| 2 | 103 ÷ 64 = 1 remainder 39 |
| 3 | 64 ÷ 39 = 1 remainder 25 |
| 4 | 39 ÷ 25 = 1 remainder 14 |
| 5 | 25 ÷ 14 = 1 remainder 11 |
| 6 | 14 ÷ 11 = 1 remainder 3 |
| 7 | 11 ÷ 3 = 3 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 101 | 7272 |
| 106 and 51 | 5406 |
| 86 and 193 | 16598 |
| 112 and 25 | 2800 |
| 89 and 137 | 12193 |