Least Common Multiple (LCM) of 67 and 91
The least common multiple (LCM) of 67 and 91 is 6097.
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 91?
First, calculate the GCD of 67 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 91 = 0 remainder 67 |
| 2 | 91 ÷ 67 = 1 remainder 24 |
| 3 | 67 ÷ 24 = 2 remainder 19 |
| 4 | 24 ÷ 19 = 1 remainder 5 |
| 5 | 19 ÷ 5 = 3 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 117 | 17667 |
| 136 and 173 | 23528 |
| 117 and 184 | 21528 |
| 130 and 137 | 17810 |
| 78 and 26 | 78 |