Least Common Multiple (LCM) of 68 and 143
The least common multiple (LCM) of 68 and 143 is 9724.
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 143?
First, calculate the GCD of 68 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 143 = 0 remainder 68 |
| 2 | 143 ÷ 68 = 2 remainder 7 |
| 3 | 68 ÷ 7 = 9 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 120 | 4920 |
| 198 and 13 | 2574 |
| 22 and 112 | 1232 |
| 99 and 157 | 15543 |
| 100 and 165 | 3300 |