Least Common Multiple (LCM) of 121 and 67
The least common multiple (LCM) of 121 and 67 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 121 and 67?
First, calculate the GCD of 121 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 67 = 1 remainder 54 |
| 2 | 67 ÷ 54 = 1 remainder 13 |
| 3 | 54 ÷ 13 = 4 remainder 2 |
| 4 | 13 ÷ 2 = 6 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 37 | 1813 |
| 16 and 48 | 48 |
| 42 and 145 | 6090 |
| 193 and 185 | 35705 |
| 131 and 128 | 16768 |