Least Common Multiple (LCM) of 143 and 68
The least common multiple (LCM) of 143 and 68 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 143 and 68?
First, calculate the GCD of 143 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 68 = 2 remainder 7 |
| 2 | 68 ÷ 7 = 9 remainder 5 |
| 3 | 7 ÷ 5 = 1 remainder 2 |
| 4 | 5 ÷ 2 = 2 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 72 | 2088 |
| 142 and 125 | 17750 |
| 52 and 159 | 8268 |
| 132 and 108 | 1188 |
| 10 and 169 | 1690 |