Least Common Multiple (LCM) of 67 and 138
The least common multiple (LCM) of 67 and 138 is 9246.
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 138?
First, calculate the GCD of 67 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 138 = 0 remainder 67 |
| 2 | 138 ÷ 67 = 2 remainder 4 |
| 3 | 67 ÷ 4 = 16 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 106 | 3074 |
| 35 and 66 | 2310 |
| 136 and 192 | 3264 |
| 11 and 11 | 11 |
| 48 and 185 | 8880 |