Least Common Multiple (LCM) of 67 and 118
The least common multiple (LCM) of 67 and 118 is 7906.
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 118?
First, calculate the GCD of 67 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 118 = 0 remainder 67 |
| 2 | 118 ÷ 67 = 1 remainder 51 |
| 3 | 67 ÷ 51 = 1 remainder 16 |
| 4 | 51 ÷ 16 = 3 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 137 | 23838 |
| 16 and 192 | 192 |
| 20 and 62 | 620 |
| 147 and 80 | 11760 |
| 14 and 140 | 140 |