Least Common Multiple (LCM) of 26 and 85
The least common multiple (LCM) of 26 and 85 is 2210.
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 85?
First, calculate the GCD of 26 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 85 = 0 remainder 26 |
| 2 | 85 ÷ 26 = 3 remainder 7 |
| 3 | 26 ÷ 7 = 3 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 138 | 3588 |
| 156 and 188 | 7332 |
| 25 and 197 | 4925 |
| 32 and 114 | 1824 |
| 160 and 105 | 3360 |