Least Common Multiple (LCM) of 67 and 121
The least common multiple (LCM) of 67 and 121 is 8107.
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 121?
First, calculate the GCD of 67 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 121 = 0 remainder 67 |
| 2 | 121 ÷ 67 = 1 remainder 54 |
| 3 | 67 ÷ 54 = 1 remainder 13 |
| 4 | 54 ÷ 13 = 4 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 75 | 11100 |
| 122 and 142 | 8662 |
| 47 and 49 | 2303 |
| 176 and 170 | 14960 |
| 151 and 114 | 17214 |