Least Common Multiple (LCM) of 109 and 37
The least common multiple (LCM) of 109 and 37 is 4033.
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 37?
First, calculate the GCD of 109 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 37 = 2 remainder 35 |
| 2 | 37 ÷ 35 = 1 remainder 2 |
| 3 | 35 ÷ 2 = 17 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 166 | 9130 |
| 142 and 26 | 1846 |
| 160 and 196 | 7840 |
| 136 and 165 | 22440 |
| 86 and 144 | 6192 |