Least Common Multiple (LCM) of 12 and 91
The least common multiple (LCM) of 12 and 91 is 1092.
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 12 and 91?
First, calculate the GCD of 12 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 12 ÷ 91 = 0 remainder 12 |
| 2 | 91 ÷ 12 = 7 remainder 7 |
| 3 | 12 ÷ 7 = 1 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 |
|---|---|
| 85 and 114 | 9690 |
| 109 and 138 | 15042 |
| 165 and 114 | 6270 |
| 131 and 166 | 21746 |
| 171 and 19 | 171 |