Least Common Multiple (LCM) of 42 and 106
The least common multiple (LCM) of 42 and 106 is 2226.
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 42 and 106?
First, calculate the GCD of 42 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 106 = 0 remainder 42 |
| 2 | 106 ÷ 42 = 2 remainder 22 |
| 3 | 42 ÷ 22 = 1 remainder 20 |
| 4 | 22 ÷ 20 = 1 remainder 2 |
| 5 | 20 ÷ 2 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 73 | 1387 |
| 35 and 40 | 280 |
| 43 and 29 | 1247 |
| 51 and 27 | 459 |
| 115 and 76 | 8740 |