Least Common Multiple (LCM) of 26 and 36
The least common multiple (LCM) of 26 and 36 is 468.
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 36?
First, calculate the GCD of 26 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 26 ÷ 36 = 0 remainder 26 |
| 2 | 36 ÷ 26 = 1 remainder 10 |
| 3 | 26 ÷ 10 = 2 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 |
|---|---|
| 195 and 105 | 1365 |
| 45 and 124 | 5580 |
| 123 and 170 | 20910 |
| 116 and 59 | 6844 |
| 43 and 24 | 1032 |