Least Common Multiple (LCM) of 31 and 143
The least common multiple (LCM) of 31 and 143 is 4433.
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 31 and 143?
First, calculate the GCD of 31 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 31 ÷ 143 = 0 remainder 31 |
| 2 | 143 ÷ 31 = 4 remainder 19 |
| 3 | 31 ÷ 19 = 1 remainder 12 |
| 4 | 19 ÷ 12 = 1 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 38 | 2432 |
| 189 and 106 | 20034 |
| 44 and 102 | 2244 |
| 161 and 57 | 9177 |
| 123 and 98 | 12054 |