Least Common Multiple (LCM) of 67 and 136
The least common multiple (LCM) of 67 and 136 is 9112.
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 136?
First, calculate the GCD of 67 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 136 = 0 remainder 67 |
| 2 | 136 ÷ 67 = 2 remainder 2 |
| 3 | 67 ÷ 2 = 33 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 149 | 15645 |
| 99 and 56 | 5544 |
| 173 and 164 | 28372 |
| 183 and 132 | 8052 |
| 189 and 71 | 13419 |