Least Common Multiple (LCM) of 67 and 161
The least common multiple (LCM) of 67 and 161 is 10787.
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 161?
First, calculate the GCD of 67 and 161 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 161 = 0 remainder 67 |
| 2 | 161 ÷ 67 = 2 remainder 27 |
| 3 | 67 ÷ 27 = 2 remainder 13 |
| 4 | 27 ÷ 13 = 2 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 172 | 8428 |
| 120 and 91 | 10920 |
| 104 and 193 | 20072 |
| 49 and 116 | 5684 |
| 128 and 144 | 1152 |