Least Common Multiple (LCM) of 39 and 100
The least common multiple (LCM) of 39 and 100 is 3900.
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 100?
First, calculate the GCD of 39 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 100 = 0 remainder 39 |
| 2 | 100 ÷ 39 = 2 remainder 22 |
| 3 | 39 ÷ 22 = 1 remainder 17 |
| 4 | 22 ÷ 17 = 1 remainder 5 |
| 5 | 17 ÷ 5 = 3 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 109 | 15696 |
| 158 and 78 | 6162 |
| 130 and 89 | 11570 |
| 155 and 43 | 6665 |
| 188 and 55 | 10340 |