Least Common Multiple (LCM) of 26 and 42
The least common multiple (LCM) of 26 and 42 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 26 and 42?
First, calculate the GCD of 26 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 42 = 0 remainder 26 |
| 2 | 42 ÷ 26 = 1 remainder 16 |
| 3 | 26 ÷ 16 = 1 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 102 | 4794 |
| 102 and 200 | 10200 |
| 14 and 185 | 2590 |
| 199 and 112 | 22288 |
| 43 and 69 | 2967 |