Least Common Multiple (LCM) of 101 and 143
The least common multiple (LCM) of 101 and 143 is 14443.
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 101 and 143?
First, calculate the GCD of 101 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 143 = 0 remainder 101 |
| 2 | 143 ÷ 101 = 1 remainder 42 |
| 3 | 101 ÷ 42 = 2 remainder 17 |
| 4 | 42 ÷ 17 = 2 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 89 | 9167 |
| 118 and 129 | 15222 |
| 179 and 82 | 14678 |
| 168 and 89 | 14952 |
| 180 and 161 | 28980 |