Least Common Multiple (LCM) of 68 and 133
The least common multiple (LCM) of 68 and 133 is 9044.
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 68 and 133?
First, calculate the GCD of 68 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 133 = 0 remainder 68 |
| 2 | 133 ÷ 68 = 1 remainder 65 |
| 3 | 68 ÷ 65 = 1 remainder 3 |
| 4 | 65 ÷ 3 = 21 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 199 | 12736 |
| 178 and 27 | 4806 |
| 70 and 36 | 1260 |
| 16 and 200 | 400 |
| 31 and 137 | 4247 |