Least Common Multiple (LCM) of 67 and 93
The least common multiple (LCM) of 67 and 93 is 6231.
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 93?
First, calculate the GCD of 67 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 93 = 0 remainder 67 |
| 2 | 93 ÷ 67 = 1 remainder 26 |
| 3 | 67 ÷ 26 = 2 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 58 | 5162 |
| 54 and 84 | 756 |
| 114 and 45 | 1710 |
| 66 and 123 | 2706 |
| 150 and 200 | 600 |