Least Common Multiple (LCM) of 39 and 102
The least common multiple (LCM) of 39 and 102 is 1326.
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 102?
First, calculate the GCD of 39 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 102 = 0 remainder 39 |
| 2 | 102 ÷ 39 = 2 remainder 24 |
| 3 | 39 ÷ 24 = 1 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 175 | 24150 |
| 78 and 114 | 1482 |
| 59 and 25 | 1475 |
| 69 and 51 | 1173 |
| 166 and 94 | 7802 |