Least Common Multiple (LCM) of 91 and 144
The least common multiple (LCM) of 91 and 144 is 13104.
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 91 and 144?
First, calculate the GCD of 91 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 144 = 0 remainder 91 |
| 2 | 144 ÷ 91 = 1 remainder 53 |
| 3 | 91 ÷ 53 = 1 remainder 38 |
| 4 | 53 ÷ 38 = 1 remainder 15 |
| 5 | 38 ÷ 15 = 2 remainder 8 |
| 6 | 15 ÷ 8 = 1 remainder 7 |
| 7 | 8 ÷ 7 = 1 remainder 1 |
| 8 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 33 | 3696 |
| 123 and 172 | 21156 |
| 16 and 42 | 336 |
| 186 and 182 | 16926 |
| 22 and 112 | 1232 |