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 |
|---|---|
| 137 and 106 | 14522 |
| 66 and 152 | 5016 |
| 131 and 188 | 24628 |
| 192 and 16 | 192 |
| 139 and 68 | 9452 |