Least Common Multiple (LCM) of 143 and 31
The least common multiple (LCM) of 143 and 31 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 143 and 31?
First, calculate the GCD of 143 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 31 = 4 remainder 19 |
| 2 | 31 ÷ 19 = 1 remainder 12 |
| 3 | 19 ÷ 12 = 1 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 146 | 13578 |
| 187 and 189 | 35343 |
| 151 and 25 | 3775 |
| 119 and 109 | 12971 |
| 120 and 174 | 3480 |