Least Common Multiple (LCM) of 72 and 191
The least common multiple (LCM) of 72 and 191 is 13752.
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 72 and 191?
First, calculate the GCD of 72 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 191 = 0 remainder 72 |
| 2 | 191 ÷ 72 = 2 remainder 47 |
| 3 | 72 ÷ 47 = 1 remainder 25 |
| 4 | 47 ÷ 25 = 1 remainder 22 |
| 5 | 25 ÷ 22 = 1 remainder 3 |
| 6 | 22 ÷ 3 = 7 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 70 | 7490 |
| 143 and 72 | 10296 |
| 168 and 106 | 8904 |
| 80 and 116 | 2320 |
| 165 and 86 | 14190 |