Least Common Multiple (LCM) of 114 and 67
The least common multiple (LCM) of 114 and 67 is 7638.
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 114 and 67?
First, calculate the GCD of 114 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 67 = 1 remainder 47 |
| 2 | 67 ÷ 47 = 1 remainder 20 |
| 3 | 47 ÷ 20 = 2 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 39 | 1794 |
| 194 and 117 | 22698 |
| 37 and 18 | 666 |
| 149 and 166 | 24734 |
| 111 and 64 | 7104 |