Least Common Multiple (LCM) of 143 and 106
The least common multiple (LCM) of 143 and 106 is 15158.
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 106?
First, calculate the GCD of 143 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 106 = 1 remainder 37 |
| 2 | 106 ÷ 37 = 2 remainder 32 |
| 3 | 37 ÷ 32 = 1 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 50 | 100 |
| 50 and 154 | 3850 |
| 55 and 30 | 330 |
| 21 and 38 | 798 |
| 46 and 136 | 3128 |