Least Common Multiple (LCM) of 39 and 77
The least common multiple (LCM) of 39 and 77 is 3003.
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 77?
First, calculate the GCD of 39 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 77 = 0 remainder 39 |
| 2 | 77 ÷ 39 = 1 remainder 38 |
| 3 | 39 ÷ 38 = 1 remainder 1 |
| 4 | 38 ÷ 1 = 38 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 78 | 8814 |
| 39 and 83 | 3237 |
| 160 and 42 | 3360 |
| 46 and 132 | 3036 |
| 158 and 75 | 11850 |