Least Common Multiple (LCM) of 67 and 191
The least common multiple (LCM) of 67 and 191 is 12797.
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 67 and 191?
First, calculate the GCD of 67 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 191 = 0 remainder 67 |
| 2 | 191 ÷ 67 = 2 remainder 57 |
| 3 | 67 ÷ 57 = 1 remainder 10 |
| 4 | 57 ÷ 10 = 5 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 15 | 525 |
| 98 and 119 | 1666 |
| 75 and 46 | 3450 |
| 114 and 125 | 14250 |
| 132 and 159 | 6996 |