Least Common Multiple (LCM) of 39 and 68
The least common multiple (LCM) of 39 and 68 is 2652.
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 39 and 68?
First, calculate the GCD of 39 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 68 = 0 remainder 39 |
| 2 | 68 ÷ 39 = 1 remainder 29 |
| 3 | 39 ÷ 29 = 1 remainder 10 |
| 4 | 29 ÷ 10 = 2 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 33 | 4983 |
| 52 and 135 | 7020 |
| 157 and 146 | 22922 |
| 49 and 187 | 9163 |
| 124 and 122 | 7564 |