Least Common Multiple (LCM) of 39 and 110
The least common multiple (LCM) of 39 and 110 is 4290.
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 110?
First, calculate the GCD of 39 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 39 ÷ 110 = 0 remainder 39 |
| 2 | 110 ÷ 39 = 2 remainder 32 |
| 3 | 39 ÷ 32 = 1 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 115 | 16905 |
| 58 and 162 | 4698 |
| 70 and 90 | 630 |
| 106 and 116 | 6148 |
| 105 and 45 | 315 |