Least Common Multiple (LCM) of 106 and 43
The least common multiple (LCM) of 106 and 43 is 4558.
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 106 and 43?
First, calculate the GCD of 106 and 43 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 43 = 2 remainder 20 |
| 2 | 43 ÷ 20 = 2 remainder 3 |
| 3 | 20 ÷ 3 = 6 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 21 | 3360 |
| 25 and 154 | 3850 |
| 174 and 65 | 11310 |
| 167 and 77 | 12859 |
| 119 and 132 | 15708 |