Least Common Multiple (LCM) of 42 and 26
The least common multiple (LCM) of 42 and 26 is 546.
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 26?
First, calculate the GCD of 42 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 26 = 1 remainder 16 |
| 2 | 26 ÷ 16 = 1 remainder 10 |
| 3 | 16 ÷ 10 = 1 remainder 6 |
| 4 | 10 ÷ 6 = 1 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 159 | 13038 |
| 12 and 167 | 2004 |
| 199 and 112 | 22288 |
| 167 and 182 | 30394 |
| 83 and 189 | 15687 |