Least Common Multiple (LCM) of 109 and 46
The least common multiple (LCM) of 109 and 46 is 5014.
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 46?
First, calculate the GCD of 109 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 46 = 2 remainder 17 |
| 2 | 46 ÷ 17 = 2 remainder 12 |
| 3 | 17 ÷ 12 = 1 remainder 5 |
| 4 | 12 ÷ 5 = 2 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 175 | 23450 |
| 32 and 48 | 96 |
| 108 and 95 | 10260 |
| 179 and 135 | 24165 |
| 107 and 59 | 6313 |