Least Common Multiple (LCM) of 144 and 91
The least common multiple (LCM) of 144 and 91 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 144 and 91?
First, calculate the GCD of 144 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 91 = 1 remainder 53 |
| 2 | 91 ÷ 53 = 1 remainder 38 |
| 3 | 53 ÷ 38 = 1 remainder 15 |
| 4 | 38 ÷ 15 = 2 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 126 | 1134 |
| 17 and 31 | 527 |
| 158 and 58 | 4582 |
| 101 and 182 | 18382 |
| 149 and 195 | 29055 |