Least Common Multiple (LCM) of 39 and 60
The least common multiple (LCM) of 39 and 60 is 780.
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 60?
First, calculate the GCD of 39 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 60 = 0 remainder 39 |
| 2 | 60 ÷ 39 = 1 remainder 21 |
| 3 | 39 ÷ 21 = 1 remainder 18 |
| 4 | 21 ÷ 18 = 1 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 61 | 1403 |
| 113 and 140 | 15820 |
| 177 and 103 | 18231 |
| 189 and 187 | 35343 |
| 68 and 147 | 9996 |