Least Common Multiple (LCM) of 67 and 39
The least common multiple (LCM) of 67 and 39 is 2613.
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 39?
First, calculate the GCD of 67 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 39 = 1 remainder 28 |
| 2 | 39 ÷ 28 = 1 remainder 11 |
| 3 | 28 ÷ 11 = 2 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 57 | 6726 |
| 164 and 72 | 2952 |
| 59 and 118 | 118 |
| 150 and 68 | 5100 |
| 142 and 193 | 27406 |