Least Common Multiple (LCM) of 67 and 34
The least common multiple (LCM) of 67 and 34 is 2278.
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 34?
First, calculate the GCD of 67 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 34 = 1 remainder 33 |
| 2 | 34 ÷ 33 = 1 remainder 1 |
| 3 | 33 ÷ 1 = 33 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 78 | 3198 |
| 157 and 176 | 27632 |
| 155 and 30 | 930 |
| 156 and 119 | 18564 |
| 159 and 136 | 21624 |