Least Common Multiple (LCM) of 36 and 91
The least common multiple (LCM) of 36 and 91 is 3276.
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 36 and 91?
First, calculate the GCD of 36 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 91 = 0 remainder 36 |
| 2 | 91 ÷ 36 = 2 remainder 19 |
| 3 | 36 ÷ 19 = 1 remainder 17 |
| 4 | 19 ÷ 17 = 1 remainder 2 |
| 5 | 17 ÷ 2 = 8 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 107 | 107 |
| 47 and 38 | 1786 |
| 37 and 131 | 4847 |
| 190 and 89 | 16910 |
| 187 and 131 | 24497 |