Least Common Multiple (LCM) of 109 and 42
The least common multiple (LCM) of 109 and 42 is 4578.
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 109 and 42?
First, calculate the GCD of 109 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 42 = 2 remainder 25 |
| 2 | 42 ÷ 25 = 1 remainder 17 |
| 3 | 25 ÷ 17 = 1 remainder 8 |
| 4 | 17 ÷ 8 = 2 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 135 | 270 |
| 160 and 176 | 1760 |
| 115 and 31 | 3565 |
| 95 and 45 | 855 |
| 199 and 18 | 3582 |