Least Common Multiple (LCM) of 67 and 168
The least common multiple (LCM) of 67 and 168 is 11256.
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 168?
First, calculate the GCD of 67 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 168 = 0 remainder 67 |
| 2 | 168 ÷ 67 = 2 remainder 34 |
| 3 | 67 ÷ 34 = 1 remainder 33 |
| 4 | 34 ÷ 33 = 1 remainder 1 |
| 5 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 124 | 6200 |
| 21 and 123 | 861 |
| 58 and 108 | 3132 |
| 81 and 176 | 14256 |
| 85 and 101 | 8585 |