Least Common Multiple (LCM) of 143 and 178
The least common multiple (LCM) of 143 and 178 is 25454.
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 178?
First, calculate the GCD of 143 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 178 = 0 remainder 143 |
| 2 | 178 ÷ 143 = 1 remainder 35 |
| 3 | 143 ÷ 35 = 4 remainder 3 |
| 4 | 35 ÷ 3 = 11 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 108 | 8964 |
| 141 and 31 | 4371 |
| 130 and 66 | 4290 |
| 109 and 161 | 17549 |
| 57 and 165 | 3135 |