Least Common Multiple (LCM) of 26 and 37
The least common multiple (LCM) of 26 and 37 is 962.
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 37?
First, calculate the GCD of 26 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 37 = 0 remainder 26 |
| 2 | 37 ÷ 26 = 1 remainder 11 |
| 3 | 26 ÷ 11 = 2 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 129 | 1806 |
| 188 and 180 | 8460 |
| 169 and 157 | 26533 |
| 75 and 76 | 5700 |
| 28 and 144 | 1008 |